



@book{ Romero,
  author =           {Romero,  A.  and  Heras, J. and Mata, G. and Rubio, J.
                      and Sergereart, F.},
  title =            {Spectral  sequences  for computing persistent homology
                      of digital images},
  publisher =        {Proceedings ACA 2013},
  year =             {2013},
  printedkey =       {RHMRS13}
}
@book{ Gangl,
  author =           {Dutour  Sikiric, M. and Gangl, H. and Gunnells, P. and
                      Hanke, J. and Schuermann, A. and Yasaki, D.},
  title =            {On  the  cohomology  of  linear  groups over imaginary
                      quadratic fields.},
  publisher =        {J. Pure and Applied Algebra, volume 220, issue 7},
  year =             {2016},
  printedkey =       {SGGHSY16}
}
@book{ Schwermer,
  author =           {Schwermer, J. and Vogtmann, K.},
  title =            {The  Integral  Homology  of  SL2 and PSL2 of Euclidean
                      Imaginary Quadratic Integer},
  publisher =        {Comment. Math. Helvetica 58},
  year =             {1983},
  printedkey =       {SV83}
}
@book{ Vogtmann,
  author =           {Vogtmann, K.},
  title =            {Cohomology of Bianchi Groups, Math.},
  publisher =        {Math. Ann. 272},
  year =             {1985},
  printedkey =       {Vog85}
}
@book{ Berkove00,
  author =           {Berkove, E.},
  title =            {On  the  Mod\texttt{\symbol{45}}2  Cohomology  of  the
                      Bianchi Groups},
  publisher =        {Trans. of the AMS., 352, no. 10},
  year =             {2000},
  printedkey =       {Ber00}
}
@book{ Berkove06,
  author =           {Berkove, E.},
  title =            {The integral Cohomology of the Bianchi Groups},
  publisher =        {Trans. of the AMS., 358, no. 3},
  year =             {2006},
  printedkey =       {Ber06}
}
@book{ Rahm13,
  author =           {Rahm, A.},
  title =            {The  homological  torsion  of  PSL2  of  the imaginary
                      quadratic integers},
  publisher =        {Trans. Amer. Math. Soc. 365},
  year =             {2013},
  printedkey =       {Rah13}
}
@book{ Rahm11,
  author =           {Rahm, A. and Fuchs, M.},
  title =            {The  integral  homology of PSL2 of imaginary quadratic
                      integers with nontrivial class group},
  publisher =        {J. Pure Appl. Algebra 215},
  year =             {2013},
  printedkey =       {RF13}
}
@book{ Rahm13a,
  author =           {Rahm, A.},
  title =            {Higher  torsion  in  the  Abelianization  of  the full
                      Bianchi groups},
  publisher =        {LMS J. Comput. Math. 16},
  year =             {2013},
  printedkey =       {Rah13}
}
@book{ Rahm20,
  author =           {Berkove, E. and Lakeland, G. and Rahm, A.},
  title =            {The  mod2  cohomology rings of congruence subgroups in
                      the Bianchi groups},
  publisher =        {J. Algebraic Combin. 52},
  year =             {2020},
  printedkey =       {BLR20}
}
@book{ Symmonds,
  author =           {Symmonds, P.},
  title =            {ON      THE     CASTELNUOVO\texttt{\symbol{45}}MUMFORD
                      REGULARITY OF THE COHOMOLOGY RING OF A GROUP},
  publisher =        {Journal  of  the Americal Mathematical Society, Volume
                      23},
  year =             {2010},
  printedkey =       {Sym10}
}
@book{ Wustner,
  author =           {Wuestner, M.},
  title =            {An example of a nonsolvable Lie algebra},
  publisher =        {Seminar Sophus Lie 2, 57\texttt{\symbol{45}}58},
  year =             {1992},
  printedkey =       {Wue92}
}
@book{ igusa,
  author =           {Igusa, K. and Orr, K. E.},
  title =            {Links, pictures and the homology of nilpotent groups},
  publisher =        {Topology,        Volume       40,       Issue       6,
                      pp\texttt{\symbol{45}}1125\texttt{\symbol{45}}\texttt{\symbol{45}}1166},
  year =             {2001},
  printedkey =       {IO01}
}
@book{ kuzmin,
  author =           {Kuz'min, Y. V. and Semenov, Y. S.},
  title =            {On the homology of a free nilpotent group of class 2},
  publisher =        {Mat.        Sb.       189,       no.       4,       pp
                      49\texttt{\symbol{45}}\texttt{\symbol{45}}82},
  year =             {1998},
  printedkey =       {KS98}
}
@book{ thurston,
  author =           {Thurston, W.},
  title =            {The        Geometry        and       Topology       of
                      Three\texttt{\symbol{45}}Manifolds},
  publisher =        {http://www.msri.org/publications/books/gt3m/},
  year =             {2002},
  printedkey =       {Thu02}
}
@book{ goncalves,
  author =           {Goncalves, D. and Martins, S.},
  title =            {Diagonal  approximation and the cohomology ring of the
                      fundamental groups of surfaces},
  publisher =        {European      Journal      of      Mathematics,     1,
                      pp122\texttt{\symbol{45}}\texttt{\symbol{45}}137},
  year =             {2015},
  printedkey =       {GM15}
}
@book{ coeurjolly,
  author =           {Coeurjolly,   D.   and   Kerautret,  B.  and  Lachaud,
                      J.\texttt{\symbol{45}}O.},
  title =            {Extraction    of    Connected   Region   Boundary   in
                      Multidimensional Images},
  publisher =        {Image Processing On Line},
  year =             {2014},
  printedkey =       {CKL14}
}
@book{ MartinFTM01,
  author =           {Martin, D. and Fowlkes, C. and Tal, D. and Malik, J.},
  title =            {A  Database  of Human Segmented Natural Images and its
                      Application  to Evaluating Segmentation Algorithms and
                      Measuring Ecological Statistics},
  publisher =        {Proc.   8th   Int'l   Conf.  Computer  Vision,  2,  pp
                      416\texttt{\symbol{45}}\texttt{\symbol{45}}423},
  year =             {2001},
  printedkey =       {MFTM01}
}
@book{ johnson,
  author =           {Johnson, F.},
  title =            {Syzygies and dihedral resolutions for dihedral groups},
  publisher =        {Communication      in      Algebra      44(5),      pp
                      2034\texttt{\symbol{45}}2047},
  year =             {2016},
  printedkey =       {Joh16}
}
@book{ kholodna,
  author =           {Kholodna, I.},
  title =            {Low\texttt{\symbol{45}}dimensional         homotopical
                      syzygies},
  publisher =        {PhD Thesis, National University of Ireland Galway},
  year =             {2001},
  printedkey =       {Kho01}
}
@book{ swan2,
  author =           {Swan, R.},
  title =            {Periodic resolutions for finite groups},
  publisher =        {Annals       of       Mathematics       72,      pages
                      267\texttt{\symbol{45}}291},
  year =             {1960},
  printedkey =       {Swa60}
}
@book{ swanB,
  author =           {Swan, R.},
  title =            {Generators  and  relations  for certain Special Linear
                      Groups},
  publisher =        {Advances           in          Mathematics          6,
                      1\texttt{\symbol{45}}\texttt{\symbol{45}}77},
  year =             {1971},
  printedkey =       {Swa71}
}
@book{ greene,
  author =           {Greene, J.},
  title =            {The lens space realization problem},
  publisher =        {Annals       of       Mathematics      177,      pages
                      449\texttt{\symbol{45}}511},
  year =             {2013},
  printedkey =       {Gre13}
}
@book{ lmoser,
  author =           {Moser, L.},
  title =            {Elementary surgery along a torus knot},
  publisher =        {Pacific Journal of Mathematics, Vol. 38, No. 3},
  year =             {1971},
  printedkey =       {Mos71}
}
@book{ horadam,
  author =           {Horadam, K.},
  title =            {An   introduction  to  cocyclic  generalised  Hadamard
                      matrices},
  publisher =        {Discrete Applied Math, 102, 115\texttt{\symbol{45}}130},
  year =             {2000},
  printedkey =       {Hor00}
}
@book{ dpr,
  author =           {Dijkgraaf, R. and Pasquier, V. and Roche, P.},
  title =            {Quasi\texttt{\symbol{45}}Hopf      algebras,     group
                      cohomology and orbifold models},
  publisher =        {Nuclear      Phys.     B     Proc.     Suppl.     18B,
                      60\texttt{\symbol{45}}72},
  year =             {1991},
  printedkey =       {DPR91}
}
@book{ brody,
  author =           {Brody, E.},
  title =            {The topological classification of the lens spaces},
  publisher =        {Ann. of Math. 71, 163{\textendash}184},
  year =             {1960},
  printedkey =       {Bro60}
}
@book{ reidemeister,
  author =           {Reidemeister, K.},
  title =            {Homotopieringe und Linsenraume},
  publisher =        {Abh. Math. Sem. Univ. Hamburg 11 , 102{\textendash}109},
  year =             {1935},
  printedkey =       {Rei35}
}
@book{ moise,
  author =           {Moise, E.},
  title =            {Affine structures in 3\texttt{\symbol{45}}manifolds V.
                      The          triangulation         theorem         and
                      Hauptvermu\texttt{\symbol{45}} tung},
  publisher =        {Annals             of             Math.            56,
                      96\texttt{\symbol{45}}\texttt{\symbol{45}}114},
  year =             {1952},
  printedkey =       {Moi52}
}
@book{ przytycki,
  author =           {Przytycki, J. and Yasukhara, A.},
  title =            {Symmetry of links and classification of lens spaces},
  publisher =        {Geom.                   Dedicata                   98,
                      57\texttt{\symbol{45}}\texttt{\symbol{45}}61},
  year =             {2003},
  printedkey =       {PY03}
}
@book{ tomoda,
  author =           {Tomoda, S. and Zvengrowski, P.},
  title =            {Remarks on the cohomology of finite fundamental groups
                      of 3\texttt{\symbol{45}}manifolds},
  publisher =        {Geometry      and      Topology     Monographs     14,
                      519\texttt{\symbol{45}}556},
  year =             {2008},
  printedkey =       {TZ08}
}
@book{ spreerkhuenel,
  author =           {Spreer, J. and Khuenel, W.},
  title =            {Combinatorial properties of the K3 surface: Simplicial
                      blowups and slicings},
  publisher =        {Experimental Mathematics Volume 20 Issue 2},
  year =             {2011},
  printedkey =       {SK11}
}
@book{ milnor,
  author =           {Milnor, J.},
  title =            {On simply connected 4\texttt{\symbol{45}}manifolds},
  publisher =        {International   symposium   on   algebraic   topology,
                      Universidad  Nacional  Autonoma  de Mexico and UNESCO,
                      Mexico City},
  year =             {1958},
  printedkey =       {Mil58}
}
@book{ hatcher,
  author =           {Hatcher, A.},
  title =            {Algebraic Topology},
  publisher =        {Available online},
  year =             {2001},
  url =              {http://pi.math.cornell.edu/\texttt{\symbol{126}}hatcher/AT/ATplain.pdf},
  printedkey =       {Hat01}
}
@book{ ksontini,
  author =           {Ksontini, R.},
  title =            {Proprietes  homotopiques  du  complexe  de  Quillen du
                      groupe symetrique},
  publisher =        {These de doctorat, Universitet de Lausanne},
  year =             {2000},
  url =              {http://sma.epfl.ch/\texttt{\symbol{126}}thevenaz/theses/Ksontini{\textunderscore}thesis.pdf},
  printedkey =       {Kso00}
}
@book{ bergeron,
  author =           {Bergeron, N.},
  title =            {Torsion homology growth in arithmetic groups},
  publisher =        {EuropeanMathematical  Society,  European  Congress  of
                      Mathematicians, July 18\texttt{\symbol{45}}22},
  year =             {2016},
  url =              {https://www.ems\texttt{\symbol{45}}ph.org/books/book.php?proj{\textunderscore}nr=220},
  printedkey =       {Ber16}
}
@book{ rahmthesis,
  author =           {Rahm, A.},
  title =            {Cohomologies   and   $K$\texttt{\symbol{45}}theory  of
                      Bianchi groups using computational geometric models},
  publisher =        {These          de         doctorat,         Universite
                      Joseph\texttt{\symbol{45}}Fourier
                      \texttt{\symbol{45}}\texttt{\symbol{45}} Grenoble I},
  year =             {2010},
  url =              {https://tel.archives\texttt{\symbol{45}}ouvertes.fr/tel\texttt{\symbol{45}}00526976v6},
  printedkey =       {Rah10}
}
@book{ stein,
  author =           {Stein, W.},
  title =            {Modular forms, a computational approach},
  publisher =        {AMS Graduate Studies in Mathematics},
  volume =           {79},
  year =             {2007},
  url =              {https://wstein.org/books/modform/modform/},
  printedkey =       {Ste07}
}
@book{ wieser,
  author =           {Wieser, G.},
  title =            {Computational arithmetic of modular forms},
  publisher =        {Universitat Duisburg\texttt{\symbol{45}}Essen},
  year =             {2007/8},
  url =              {http://math.uni.lu/\texttt{\symbol{126}}wiese/notes/MFII.pdf},
  printedkey =       {Wie/8}
}
@article{ eichler,
  author =           {Eichler, M.},
  title =            {Eine Verallgemeinerung der Abelschen Integrale},
  journal =          {Mathematische Zeitschrift},
  volume =           {67},
  year =             {1957},
  pages =            {267\texttt{\symbol{45}}\texttt{\symbol{45}}298},
  issn =             {0025\texttt{\symbol{45}}5874},
  mrnumber =         {0089928},
  printedkey =       {Eic57}
}
@article{ sengun,
  author =           {Sengun, M. H.},
  title =            {On the Integral Cohomology of Bianchi Groups},
  journal =          {Experimental Mathematics},
  volume =           {20(4)},
  year =             {2011},
  pages =            {487\texttt{\symbol{45}}\texttt{\symbol{45}}505},
  issn =             {1058\texttt{\symbol{45}}6458 print},
  printedkey =       {Sen11}
}
@article{ schoennenbeck,
  author =           {Braun,   O.  and  Coulangeon,  R.  and  Nebe,  G.  and
                      Schoennenbeck, S.},
  title =            {Computing      in      arithmetic      groups     with
                      Vorono{\"\i}{\textquoteright}s algorithm},
  journal =          {J. Algebra},
  volume =           {435},
  year =             {2015},
  pages =            {263\texttt{\symbol{45}}\texttt{\symbol{45}}285},
  printedkey =       {BCNS15}
}
@article{ swan,
  author =           {Swan, R.},
  title =            {Generators  and  relations  for certain general linear
                      groups},
  journal =          {Advances in Mathematics},
  volume =           {6},
  year =             {1971},
  pages =            {1\texttt{\symbol{45}}\texttt{\symbol{45}}77},
  mrnumber =         {0284516},
  printedkey =       {Swa71}
}
@article{ atkinlehner,
  author =           {Atkin, A. and Lehner, J.},
  title =            {Hecke operators on $\Gamma_0(m)$},
  journal =          {Math. Ann.},
  volume =           {185},
  year =             {1970},
  pages =            {134\texttt{\symbol{45}}\texttt{\symbol{45}}160},
  printedkey =       {AL70}
}
@article{ kulkarni,
  author =           {Kulkarni, R.},
  title =            {An  arithmetic\texttt{\symbol{45}}geometric  method in
                      the study of the subgroups of the modular group},
  journal =          {American Journal of Mathematics},
  volume =           {113, No. 6},
  year =             {1991},
  pages =            {1053\texttt{\symbol{45}}\texttt{\symbol{45}}1133},
  url =              {https://www.jstor.org/stable/2374900},
  printedkey =       {Kul91}
}
@article{ shimura,
  author =           {Shimura, G.},
  title =            {Sur les integrales attachees aux formes automorphes},
  journal =          {Journal of the Mathematical Society of Japan},
  volume =           {67},
  year =             {1959},
  pages =            {291\texttt{\symbol{45}}\texttt{\symbol{45}}311},
  issn =             {0025\texttt{\symbol{45}}5645},
  mrnumber =         {0120372},
  printedkey =       {Shi59}
}
@article{ MR1758871,
  author =           {Satoh, S.},
  title =            {Virtual      knot      presentation      of     ribbon
                      torus\texttt{\symbol{45}}knots},
  journal =          {J. Knot Theory Ramifications},
  volume =           {9},
  number =           {4},
  year =             {2000},
  pages =            {531\texttt{\symbol{45}}\texttt{\symbol{45}}542},
  fjournal =         {Journal of Knot Theory and its Ramifications},
  issn =             {0218\texttt{\symbol{45}}2165},
  mrclass =          {57Q45 (57M25)},
  mrnumber =         {1758871},
  mrreviewer =       {Seiichi Kamada},
  url =              {https://doi.org/10.1142/S0218216500000293},
  doi =              {10.1142/S0218216500000293},
  printedkey =       {Sat00}
}
@article{ MR2441256,
  author =           {Kauffman, L. H. and Faria Martins, J.},
  title =            {Invariants  of welded virtual knots via crossed module
                      invariants of knotted surfaces},
  journal =          {Compos. Math.},
  volume =           {144},
  number =           {4},
  year =             {2008},
  pages =            {1046\texttt{\symbol{45}}\texttt{\symbol{45}}1080},
  fjournal =         {Compositio Mathematica},
  issn =             {0010\texttt{\symbol{45}}437X},
  mrclass =          {57M25 (57Q45)},
  mrnumber =         {2441256},
  mrreviewer =       {Riccardo Piergallini},
  url =              {https://doi.org/10.1112/S0010437X07003429},
  doi =              {10.1112/S0010437X07003429},
  printedkey =       {KM08}
}
@article{ buiellis,
  author =           {Bui, A. and Ellis, G.},
  title =            {The homology of $SL_2(\mathbb Z[1/m])$ for small $m$},
  journal =          {Journal of Algebra},
  volume =           {408},
  year =             {2014},
  pages =            {102\texttt{\symbol{45}}\texttt{\symbol{45}}108},
  url =              {https://www.sciencedirect.com/science/article/pii/S002186931300625X},
  printedkey =       {BE14}
}
@article{ ellisharrisskoldberg,
  author =           {Ellis, G. and Harris, J. and Skoldberg, E.},
  title =            {Polytopal resolutions for finite groups},
  journal =          {J. Reine Angew. Math.},
  volume =           {598},
  year =             {2006},
  pages =            {131\texttt{\symbol{45}}\texttt{\symbol{45}}137},
  printedkey =       {EHS06}
}
@article{ brownloday,
  author =           {Brown, R. and Loday, J.\texttt{\symbol{45}}L.},
  title =            {Van Kampen theorems for diagrams of spaces},
  journal =          {Topology},
  volume =           {26},
  year =             {1987},
  pages =            {311\texttt{\symbol{45}}\texttt{\symbol{45}}335},
  printedkey =       {BL87}
}
@article{ liuye,
  author =           {Liu, C. and Ye, W.},
  title =            {Crystallography,       Group      Cohomology,      and
                      Lieb\texttt{\symbol{45}}Schultz\texttt{\symbol{45}}Mattis
                      Constraints},
  journal =          {https://arxiv.org/abs/2410.03607/},
  year =             {2024},
  printedkey =       {LY24}
}
@article{ liuyegithub,
  author =           {Liu, C. and Ye, W.},
  title =            {Space       group       cohomology       and       LSM
                      \texttt{\symbol{45}}\texttt{\symbol{45}}    a   github
                      repository},
  journal =          {https://github.com/liuchx1993/Space\texttt{\symbol{45}}Group\texttt{\symbol{45}}Cohomology\texttt{\symbol{45}}and\texttt{\symbol{45}}LSM},
  year =             {2024},
  printedkey =       {LY24}
}
@article{ Webb,
  author =           {Webb, P.},
  title =            {Subgroup complexes},
  journal =          {Proceedings of Symposia in Pure Mathematics, Volume 47},
  year =             {1987},
  printedkey =       {Web87}
}
