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<h3>References</h3>
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[<span class='BibKey'>AL70</span>] <b class='BibAuthor'>Atkin, A. and Lehner, J.</b>,
<i class='BibTitle'>Hecke operators on Γ_0(m) </i>,
<span class='BibJournal'>Math. Ann. </span>,
<em class='BibVolume'>185</em>
(<span class='BibYear'>1970</span>),
<span class='BibPages'>134--160</span>.
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[<span class='BibKey'>BCNS15</span>] <b class='BibAuthor'>Braun, O., Coulangeon, R., Nebe, G. and Schoennenbeck, S.</b>,
<i class='BibTitle'>Computing in arithmetic groups with
Voronoï’s algorithm</i>,
<span class='BibJournal'>J. Algebra </span>,
<em class='BibVolume'>435</em>
(<span class='BibYear'>2015</span>),
<span class='BibPages'>263--285</span>.
</p>
<p><a id="biBbuiellis" name="biBbuiellis"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BE14</span>] <b class='BibAuthor'>Bui, A. and Ellis, G.</b>,
<a href="https://www.sciencedirect.com/science/article/pii/S002186931300625X"><i class='BibTitle'>The homology of SL_2( Z[1/m]) for small m </i></a>,
<span class='BibJournal'>Journal of Algebra</span>,
<em class='BibVolume'>408</em>
(<span class='BibYear'>2014</span>),
<span class='BibPages'>102--108</span>.
</p>
<p><a id="biBBerkove00" name="biBBerkove00"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Ber00</span>] <b class='BibAuthor'>Berkove, E.</b>,
<i class='BibTitle'>
On the Mod-2 Cohomology of the Bianchi Groups
</i>,
<span class='BibPublisher'>Trans. of the AMS., 352, no.
10
</span>
(<span class='BibYear'>2000</span>).
</p>
<p><a id="biBBerkove06" name="biBBerkove06"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Ber06</span>] <b class='BibAuthor'>Berkove, E.</b>,
<i class='BibTitle'>
The integral Cohomology of the Bianchi Groups
</i>,
<span class='BibPublisher'>Trans. of the AMS., 358, no.
3
</span>
(<span class='BibYear'>2006</span>).
</p>
<p><a id="biBbergeron" name="biBbergeron"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Ber16</span>] <b class='BibAuthor'>Bergeron, N.</b>,
<a href="https://www.ems-ph.org/books/book.php?proj_nr=220"><i class='BibTitle'>Torsion homology growth in arithmetic groups </i></a>,
<span class='BibPublisher'>EuropeanMathematical Society, European Congress of Mathematicians, July 18-22 </span>
(<span class='BibYear'>2016</span>).
</p>
<p><a id="biBbrownloday" name="biBbrownloday"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BL87</span>] <b class='BibAuthor'>Brown, R. and Loday, J.-L.</b>,
<i class='BibTitle'>Van Kampen theorems for diagrams of spaces </i>,
<span class='BibJournal'> Topology</span>,
<em class='BibVolume'>26</em>
(<span class='BibYear'>1987</span>),
<span class='BibPages'>311--335</span>.
</p>
<p><a id="biBRahm20" name="biBRahm20"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>BLR20</span>] <b class='BibAuthor'>Berkove, E., Lakeland, G. and Rahm, A.</b>,
<i class='BibTitle'>
The mod2 cohomology rings of congruence subgroups in the Bianchi groups
</i>,
<span class='BibPublisher'>J. Algebraic Combin. 52
</span>
(<span class='BibYear'>2020</span>).
</p>
<p><a id="biBbrody" name="biBbrody"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Bro60</span>] <b class='BibAuthor'>Brody, E.</b>,
<i class='BibTitle'>The topological classification of the lens spaces
</i>,
<span class='BibPublisher'> Ann. of Math. 71, 163–184
</span>
(<span class='BibYear'>1960</span>).
</p>
<p><a id="biBcoeurjolly" name="biBcoeurjolly"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>CKL14</span>] <b class='BibAuthor'>Coeurjolly, D., Kerautret, B. and Lachaud, J.-O.</b>,
<i class='BibTitle'>
Extraction of Connected Region Boundary in
Multidimensional Images
</i>,
<span class='BibPublisher'>Image Processing On Line
</span>
(<span class='BibYear'>2014</span>).
</p>
<p><a id="biBdpr" name="biBdpr"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DPR91</span>] <b class='BibAuthor'>Dijkgraaf, R., Pasquier, V. and Roche, P.</b>,
<i class='BibTitle'>Quasi-Hopf algebras, group cohomology and orbifold models
</i>,
<span class='BibPublisher'> Nuclear Phys. B Proc. Suppl. 18B, 60-72
</span>
(<span class='BibYear'>1991</span>).
</p>
<p><a id="biBGangl" name="biBGangl"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>DSGG+16</span>] <b class='BibAuthor'>Dutour Sikiric, M., Gangl, H., Gunnells, P., Hanke, J., Schuermann, A. and Yasaki, D.</b>,
<i class='BibTitle'> On the cohomology of linear groups over imaginary quadratic fields.
</i>,
<span class='BibPublisher'>J. Pure and Applied Algebra, volume 220, issue 7
</span>
(<span class='BibYear'>2016</span>).
</p>
<p><a id="biBellisharrisskoldberg" name="biBellisharrisskoldberg"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>EHS06</span>] <b class='BibAuthor'>Ellis, G., Harris, J. and Skoldberg, E.</b>,
<i class='BibTitle'>Polytopal resolutions for finite groups </i>,
<span class='BibJournal'> J. Reine Angew. Math.</span>,
<em class='BibVolume'>598</em>
(<span class='BibYear'>2006</span>),
<span class='BibPages'>131--137</span>.
</p>
<p><a id="biBeichler" name="biBeichler"></a></p>
<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=0089928">Eic57</a></span>] <b class='BibAuthor'>Eichler, M.</b>,
<i class='BibTitle'>Eine Verallgemeinerung der Abelschen Integrale </i>,
<span class='BibJournal'>Mathematische Zeitschrift </span>,
<em class='BibVolume'>67</em>
(<span class='BibYear'>1957</span>),
<span class='BibPages'>267--298</span>.
</p>
<p><a id="biBgoncalves" name="biBgoncalves"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>GM15</span>] <b class='BibAuthor'>Goncalves, D. and Martins, S.</b>,
<i class='BibTitle'> Diagonal approximation and the cohomology ring of the
fundamental groups of surfaces
</i>,
<span class='BibPublisher'>European Journal of Mathematics, 1, pp122--137
</span>
(<span class='BibYear'>2015</span>).
</p>
<p><a id="biBgreene" name="biBgreene"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Gre13</span>] <b class='BibAuthor'>Greene, J.</b>,
<i class='BibTitle'>The lens space realization problem
</i>,
<span class='BibPublisher'>Annals of Mathematics 177, pages 449-511
</span>
(<span class='BibYear'>2013</span>).
</p>
<p><a id="biBhatcher" name="biBhatcher"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Hat01</span>] <b class='BibAuthor'>Hatcher, A.</b>,
<a href="http://pi.math.cornell.edu/~hatcher/AT/ATplain.pdf "><i class='BibTitle'>Algebraic Topology </i></a>,
<span class='BibPublisher'>Available online </span>
(<span class='BibYear'>2001</span>).
</p>
<p><a id="biBhoradam" name="biBhoradam"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Hor00</span>] <b class='BibAuthor'>Horadam, K.</b>,
<i class='BibTitle'>An introduction to cocyclic generalised Hadamard matrices
</i>,
<span class='BibPublisher'> Discrete Applied Math, 102, 115-130
</span>
(<span class='BibYear'>2000</span>).
</p>
<p><a id="biBigusa" name="biBigusa"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>IO01</span>] <b class='BibAuthor'>Igusa, K. and Orr, K. E.</b>,
<i class='BibTitle'> Links, pictures and the homology of nilpotent groups
</i>,
<span class='BibPublisher'>Topology, Volume 40, Issue 6, pp-1125--1166
</span>
(<span class='BibYear'>2001</span>).
</p>
<p><a id="biBjohnson" name="biBjohnson"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Joh16</span>] <b class='BibAuthor'>Johnson, F.</b>,
<i class='BibTitle'>Syzygies and dihedral resolutions for dihedral groups
</i>,
<span class='BibPublisher'>Communication in Algebra 44(5), pp 2034-2047
</span>
(<span class='BibYear'>2016</span>).
</p>
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<p class='BibEntry'>
[<span class='BibKeyLink'><a href="https://www.ams.org/mathscinet-getitem?mr=2441256">KFM08</a></span>] <b class='BibAuthor'>Kauffman, L. H. and Faria Martins, J.</b>,
<a href="https://doi.org/10.1112/S0010437X07003429"><i class='BibTitle'>Invariants of welded virtual knots via crossed module
invariants of knotted surfaces</i></a>,
<span class='BibJournal'>Compos. Math.</span>,
<em class='BibVolume'>144</em> (<span class='BibNumber'>4</span>)
(<span class='BibYear'>2008</span>),
<span class='BibPages'>1046--1080</span>.
</p>
<p><a id="biBkholodna" name="biBkholodna"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Kho01</span>] <b class='BibAuthor'>Kholodna, I.</b>,
<i class='BibTitle'>Low-dimensional homotopical syzygies
</i>,
<span class='BibPublisher'>PhD Thesis, National University of Ireland Galway
</span>
(<span class='BibYear'>2001</span>).
</p>
<p><a id="biBkuzmin" name="biBkuzmin"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>KS98</span>] <b class='BibAuthor'>Kuz'min, Y. V. and Semenov, Y. S.</b>,
<i class='BibTitle'> On the homology of a free nilpotent group of class 2
</i>,
<span class='BibPublisher'>Mat. Sb. 189, no. 4, pp 49--82
</span>
(<span class='BibYear'>1998</span>).
</p>
<p><a id="biBksontini" name="biBksontini"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Kso00</span>] <b class='BibAuthor'>Ksontini, R.</b>,
<a href="http://sma.epfl.ch/~thevenaz/theses/Ksontini_thesis.pdf"><i class='BibTitle'>Proprietes homotopiques du complexe de Quillen du groupe
symetrique</i></a>,
<span class='BibPublisher'>These de doctorat, Universitet de Lausanne </span>
(<span class='BibYear'>2000</span>).
</p>
<p><a id="biBkulkarni" name="biBkulkarni"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Kul91</span>] <b class='BibAuthor'>Kulkarni, R.</b>,
<a href="https://www.jstor.org/stable/2374900"><i class='BibTitle'>An arithmetic-geometric method in the study of the subgroups of the modular group </i></a>,
<span class='BibJournal'>American Journal of Mathematics </span>,
<em class='BibVolume'>113, No. 6</em>
(<span class='BibYear'>1991</span>),
<span class='BibPages'>1053--1133</span>.
</p>
<p><a id="biBliuye" name="biBliuye"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>LY24a</span>] <b class='BibAuthor'>Liu, C. and Ye, W.</b>,
<i class='BibTitle'> Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints</i>,
<span class='BibJournal'> https://arxiv.org/abs/2410.03607/</span>
(<span class='BibYear'>2024</span>).
</p>
<p><a id="biBliuyegithub" name="biBliuyegithub"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>LY24b</span>] <b class='BibAuthor'>Liu, C. and Ye, W.</b>,
<i class='BibTitle'> Space group cohomology and LSM -- a github repository</i>,
<span class='BibJournal'> https://github.com/liuchx1993/Space-Group-Cohomology-and-LSM</span>
(<span class='BibYear'>2024</span>).
</p>
<p><a id="biBMartinFTM01" name="biBMartinFTM01"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>MFTM01</span>] <b class='BibAuthor'>Martin, D., Fowlkes, C., Tal, D. and Malik, J.</b>,
<i class='BibTitle'>
A Database of Human Segmented Natural Images and its
Application to Evaluating Segmentation Algorithms and
Measuring Ecological Statistics
</i>,
<span class='BibPublisher'>Proc. 8th Int'l Conf. Computer Vision, 2, pp 416--423
</span>
(<span class='BibYear'>2001</span>).
</p>
<p><a id="biBmilnor" name="biBmilnor"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Mil58</span>] <b class='BibAuthor'>Milnor, J.</b>,
<i class='BibTitle'>On simply connected 4-manifolds</i>,
<span class='BibPublisher'> International symposium on algebraic topology, Universidad Nacional Autonoma de Mexico and UNESCO, Mexico City</span>
(<span class='BibYear'>1958</span>).
</p>
<p><a id="biBmoise" name="biBmoise"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Moi52</span>] <b class='BibAuthor'>Moise, E.</b>,
<i class='BibTitle'>Affine structures in 3-manifolds V. The triangulation theorem and Hauptvermu-
tung</i>,
<span class='BibPublisher'> Annals of Math. 56, 96--114</span>
(<span class='BibYear'>1952</span>).
</p>
<p><a id="biBlmoser" name="biBlmoser"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Mos71</span>] <b class='BibAuthor'>Moser, L.</b>,
<i class='BibTitle'>Elementary surgery along a torus knot
</i>,
<span class='BibPublisher'>Pacific Journal of Mathematics, Vol. 38, No. 3
</span>
(<span class='BibYear'>1971</span>).
</p>
<p><a id="biBprzytycki" name="biBprzytycki"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>PY03</span>] <b class='BibAuthor'>Przytycki, J. and Yasukhara, A.</b>,
<i class='BibTitle'>Symmetry of links and classification of lens spaces</i>,
<span class='BibPublisher'> Geom. Dedicata 98, 57--61</span>
(<span class='BibYear'>2003</span>).
</p>
<p><a id="biBrahmthesis" name="biBrahmthesis"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Rah10</span>] <b class='BibAuthor'>Rahm, A.</b>,
<a href="https://tel.archives-ouvertes.fr/tel-00526976v6"><i class='BibTitle'>Cohomologies and K-theory of Bianchi groups using computational geometric models </i></a>,
<span class='BibPublisher'>These de doctorat, Universite Joseph-Fourier -- Grenoble I </span>
(<span class='BibYear'>2010</span>).
</p>
<p><a id="biBRahm13a" name="biBRahm13a"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Rah13a</span>] <b class='BibAuthor'>Rahm, A.</b>,
<i class='BibTitle'>
Higher torsion in the Abelianization of the full Bianchi groups
</i>,
<span class='BibPublisher'>LMS J. Comput. Math. 16
</span>
(<span class='BibYear'>2013</span>).
</p>
<p><a id="biBRahm13" name="biBRahm13"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Rah13b</span>] <b class='BibAuthor'>Rahm, A.</b>,
<i class='BibTitle'>
The homological torsion of PSL2 of the imaginary quadratic integers
</i>,
<span class='BibPublisher'>Trans. Amer. Math. Soc. 365
</span>
(<span class='BibYear'>2013</span>).
</p>
<p><a id="biBreidemeister" name="biBreidemeister"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>Rei35</span>] <b class='BibAuthor'>Reidemeister, K.</b>,
<i class='BibTitle'>Homotopieringe und Linsenraume
</i>,
<span class='BibPublisher'> Abh. Math. Sem. Univ. Hamburg 11
, 102–109</span>
(<span class='BibYear'>1935</span>).
</p>
<p><a id="biBRahm11" name="biBRahm11"></a></p>
<p class='BibEntry'>
[<span class='BibKey'>RF13</span>] <b class='BibAuthor'>Rahm, A. and Fuchs, M.</b>,
<i class='BibTitle'>
The integral homology of
PSL2 of imaginary quadratic integers with nontrivial class group</i>,
<span class='BibPublisher'>J. Pure Appl. Algebra 215
</span>
(<span class='BibYear'>2013</span>).
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<p> </p>
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