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<h3>References</h3>

<a id="biBatkinlehner" name="biBatkinlehner"></a>

[AL70] Atkin, A. and Lehner, J.,
Hecke operators on \(\Gamma_0(m)\) ,
Math. Ann. ,
185
(1970),
134--160.


<a id="biBschoennenbeck" name="biBschoennenbeck"></a>

[BCNS15] Braun, O., Coulangeon, R., Nebe, G. and Schoennenbeck, S.,
Computing in arithmetic groups with
Voronoï’s algorithm,
J. Algebra ,
435
(2015),
263--285.


<a id="biBbuiellis" name="biBbuiellis"></a>

[BE14] Bui, A. and Ellis, G.,
<a href="https://www.sciencedirect.com/science/article/pii/S002186931300625X">The homology of \(SL_2(\mathbb Z[1/m])\) for small \(m\) </a>,
Journal of Algebra,
408
(2014),
102--108.


<a id="biBBerkove00" name="biBBerkove00"></a>

[Ber00] Berkove, E.,

On the Mod-2 Cohomology of the Bianchi Groups
,
Trans. of the AMS., 352, no.
10

(2000).


<a id="biBBerkove06" name="biBBerkove06"></a>

[Ber06] Berkove, E.,

The integral Cohomology of the Bianchi Groups
,
Trans. of the AMS., 358, no.
3

(2006).


<a id="biBbergeron" name="biBbergeron"></a>

[Ber16] Bergeron, N.,
<a href="https://www.ems-ph.org/books/book.php?proj_nr=220">Torsion homology growth in arithmetic groups </a>,
EuropeanMathematical Society, European Congress of Mathematicians, July 18-22 
(2016).


<a id="biBbrownloday" name="biBbrownloday"></a>

[BL87] Brown, R. and Loday, J.-L.,
Van Kampen theorems for diagrams of spaces ,
 Topology,
26
(1987),
311--335.


<a id="biBRahm20" name="biBRahm20"></a>

[BLR20] Berkove, E., Lakeland, G. and Rahm, A.,

The mod2 cohomology rings of congruence subgroups in the Bianchi groups
 ,
J. Algebraic Combin. 52

(2020).


<a id="biBbrody" name="biBbrody"></a>

[Bro60] Brody, E.,
The topological classification of the lens spaces
,
 Ann. of Math. 71, 163–184

(1960).


<a id="biBcoeurjolly" name="biBcoeurjolly"></a>

[CKL14] Coeurjolly, D., Kerautret, B. and Lachaud, J.-O.,

Extraction of Connected Region Boundary in
Multidimensional Images
,
Image Processing On Line

(2014).


<a id="biBdpr" name="biBdpr"></a>

[DPR91] Dijkgraaf, R., Pasquier, V. and Roche, P.,
Quasi-Hopf algebras, group cohomology and orbifold models
,
 Nuclear Phys. B Proc. Suppl. 18B, 60-72

(1991).


<a id="biBGangl" name="biBGangl"></a>

[DSGG+16] Dutour Sikiric, M., Gangl, H., Gunnells, P., Hanke, J., Schuermann, A. and Yasaki, D.,
 On the cohomology of linear groups over imaginary quadratic fields.
,
J. Pure and Applied Algebra, volume 220, issue 7

(2016).


<a id="biBellisharrisskoldberg" name="biBellisharrisskoldberg"></a>

[EHS06] Ellis, G., Harris, J. and Skoldberg, E.,
Polytopal resolutions for finite groups ,
 J. Reine Angew. Math.,
598
(2006),
131--137.


<a id="biBeichler" name="biBeichler"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0089928">Eic57</a>] Eichler, M.,
Eine Verallgemeinerung der Abelschen Integrale ,
Mathematische Zeitschrift ,
67
(1957),
267--298.


<a id="biBgoncalves" name="biBgoncalves"></a>

[GM15] Goncalves, D. and Martins, S.,
 Diagonal approximation and the cohomology ring of the
 fundamental groups of surfaces
,
European Journal of Mathematics, 1, pp122--137

(2015).


<a id="biBgreene" name="biBgreene"></a>

[Gre13] Greene, J.,
The lens space realization problem
,
Annals of Mathematics 177, pages 449-511

(2013).


<a id="biBhatcher" name="biBhatcher"></a>

[Hat01] Hatcher, A.,
<a href="http://pi.math.cornell.edu/~hatcher/AT/ATplain.pdf ">Algebraic Topology </a>,
Available online 
(2001).


<a id="biBhoradam" name="biBhoradam"></a>

[Hor00] Horadam, K.,
An introduction to cocyclic generalised Hadamard matrices
,
 Discrete Applied Math, 102, 115-130

(2000).


<a id="biBigusa" name="biBigusa"></a>

[IO01] Igusa, K. and Orr, K. E.,
 Links, pictures and the homology of nilpotent groups
,
Topology, Volume 40, Issue 6, pp-1125--1166

(2001).


<a id="biBjohnson" name="biBjohnson"></a>

[Joh16] Johnson, F.,
Syzygies and dihedral resolutions for dihedral groups
,
Communication in Algebra 44(5), pp 2034-2047

(2016).


<a id="biBMR2441256" name="biBMR2441256"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=2441256">KFM08</a>] Kauffman, L. H. and Faria Martins, J.,
<a href="https://doi.org/10.1112/S0010437X07003429">Invariants of welded virtual knots via crossed module
 invariants of knotted surfaces</a>,
Compos. Math.,
144 (4)
(2008),
1046--1080.


<a id="biBkholodna" name="biBkholodna"></a>

[Kho01] Kholodna, I.,
Low-dimensional homotopical syzygies
,
PhD Thesis, National University of Ireland Galway

(2001).


<a id="biBkuzmin" name="biBkuzmin"></a>

[KS98] Kuz'min, Y. V. and Semenov, Y. S.,
 On the homology of a free nilpotent group of class 2
,
Mat. Sb. 189, no. 4, pp 49--82

(1998).


<a id="biBksontini" name="biBksontini"></a>

[Kso00] Ksontini, R.,
<a href="http://sma.epfl.ch/~thevenaz/theses/Ksontini_thesis.pdf">Proprietes homotopiques du complexe de Quillen du groupe
 symetrique</a>,
These de doctorat, Universitet de Lausanne 
(2000).


<a id="biBkulkarni" name="biBkulkarni"></a>

[Kul91] Kulkarni, R.,
<a href="https://www.jstor.org/stable/2374900">An arithmetic-geometric method in the study of the subgroups of the modular group </a>,
American Journal of Mathematics ,
113, No. 6
(1991),
1053--1133.


<a id="biBliuye" name="biBliuye"></a>

[LY24a] Liu, C. and Ye, W.,
 Crystallography, Group Cohomology, and Lieb-Schultz-Mattis Constraints,
 https://arxiv.org/abs/2410.03607/
(2024).


<a id="biBliuyegithub" name="biBliuyegithub"></a>

[LY24b] Liu, C. and Ye, W.,
 Space group cohomology and LSM -- a github repository,
 https://github.com/liuchx1993/Space-Group-Cohomology-and-LSM
(2024).


<a id="biBMartinFTM01" name="biBMartinFTM01"></a>

[MFTM01] Martin, D., Fowlkes, C., Tal, D. and Malik, J.,

 A Database of Human Segmented Natural Images and its
 Application to Evaluating Segmentation Algorithms and
 Measuring Ecological Statistics
,
Proc. 8th Int'l Conf. Computer Vision, 2, pp 416--423

(2001).


<a id="biBmilnor" name="biBmilnor"></a>

[Mil58] Milnor, J.,
On simply connected 4-manifolds,
 International symposium on algebraic topology, Universidad Nacional Autonoma de Mexico and UNESCO, Mexico City
(1958).


<a id="biBmoise" name="biBmoise"></a>

[Moi52] Moise, E.,
Affine structures in 3-manifolds V. The triangulation theorem and Hauptvermu-
tung,
 Annals of Math. 56, 96--114
(1952).


<a id="biBlmoser" name="biBlmoser"></a>

[Mos71] Moser, L.,
Elementary surgery along a torus knot
,
Pacific Journal of Mathematics, Vol. 38, No. 3

(1971).


<a id="biBprzytycki" name="biBprzytycki"></a>

[PY03] Przytycki, J. and Yasukhara, A.,
Symmetry of links and classification of lens spaces,
 Geom. Dedicata 98, 57--61
(2003).


<a id="biBrahmthesis" name="biBrahmthesis"></a>

[Rah10] Rahm, A.,
<a href="https://tel.archives-ouvertes.fr/tel-00526976v6">Cohomologies and \(K\)-theory of Bianchi groups using computational geometric models </a>,
These de doctorat, Universite Joseph-Fourier -- Grenoble I 
(2010).


<a id="biBRahm13a" name="biBRahm13a"></a>

[Rah13a] Rahm, A.,

 Higher torsion in the Abelianization of the full Bianchi groups
 ,
LMS J. Comput. Math. 16

(2013).


<a id="biBRahm13" name="biBRahm13"></a>

[Rah13b] Rahm, A.,

 The homological torsion of PSL2 of the imaginary quadratic integers
 ,
Trans. Amer. Math. Soc. 365

(2013).


<a id="biBreidemeister" name="biBreidemeister"></a>

[Rei35] Reidemeister, K.,
Homotopieringe und Linsenraume
,
 Abh. Math. Sem. Univ. Hamburg 11
, 102–109
(1935).


<a id="biBRahm11" name="biBRahm11"></a>

[RF13] Rahm, A. and Fuchs, M.,

The integral homology of
PSL2 of imaginary quadratic integers with nontrivial class group,
J. Pure Appl. Algebra 215

(2013).


<a id="biBMR1758871" name="biBMR1758871"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=1758871">Sat00</a>] Satoh, S.,
<a href="https://doi.org/10.1142/S0218216500000293">Virtual knot presentation of ribbon torus-knots</a>,
J. Knot Theory Ramifications,
9 (4)
(2000),
531--542.


<a id="biBsengun" name="biBsengun"></a>

[Sen11] Sengun, M. H.,
On the Integral Cohomology of Bianchi Groups ,
Experimental Mathematics ,
20(4)
(2011),
487--505.


<a id="biBshimura" name="biBshimura"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=">Shi59</a>] Shimura, G.,
Sur les integrales attachees aux formes automorphes ,
Journal of the Mathematical Society of Japan ,
67
(1959),
291--311.


<a id="biBspreerkhuenel" name="biBspreerkhuenel"></a>

[SK11] Spreer, J. and Khuenel, W.,
Combinatorial properties of the K3 surface: Simplicial blowups and slicings,
 Experimental Mathematics Volume 20 Issue 2
(2011).


<a id="biBstein" name="biBstein"></a>

[Ste07] Stein, W.,
<a href="https://wstein.org/books/modform/modform/">Modular forms, a computational approach </a>,
AMS Graduate Studies in Mathematics ,
79
(2007).


<a id="biBSchwermer" name="biBSchwermer"></a>

[SV83] Schwermer, J. and Vogtmann, K.,
 The Integral Homology of SL2 and PSL2 of Euclidean
Imaginary Quadratic Integer
,
Comment. Math. Helvetica 58

(1983).


<a id="biBswan2" name="biBswan2"></a>

[Swa60] Swan, R.,
Periodic resolutions for finite groups
,
Annals of Mathematics 72, pages 267-291

(1960).


<a id="biBswan" name="biBswan"></a>

[<a href="https://www.ams.org/mathscinet-getitem?mr=0284516">Swa71a</a>] Swan, R.,
Generators and relations for certain general linear groups ,
Advances in Mathematics ,
6
(1971),
1--77.


<a id="biBswanB" name="biBswanB"></a>

[Swa71b] Swan, R.,
Generators and relations for certain Special Linear Groups
,
Advances in Mathematics 6, 1--77

(1971).


<a id="biBSymmonds" name="biBSymmonds"></a>

[Sym10] Symmonds, P.,
 ON THE CASTELNUOVO-MUMFORD REGULARITY OF THE COHOMOLOGY RING OF A GROUP
,
Journal of the Americal Mathematical Society, Volume 23

(2010).


<a id="biBthurston" name="biBthurston"></a>

[Thu02] Thurston, W.,
 The Geometry and Topology of Three-Manifolds
,
http://www.msri.org/publications/books/gt3m/

(2002).


<a id="biBtomoda" name="biBtomoda"></a>

[TZ08] Tomoda, S. and Zvengrowski, P.,
Remarks on the cohomology of finite fundamental groups of 3-manifolds,
 Geometry and Topology Monographs 14, 519-556
(2008).


<a id="biBVogtmann" name="biBVogtmann"></a>

[Vog85] Vogtmann, K.,

Cohomology of Bianchi Groups, Math.
,
Math. Ann. 272

(1985).


<a id="biBWebb" name="biBWebb"></a>

[Web87] Webb, P.,
 Subgroup complexes,
 Proceedings of Symposia
in Pure Mathematics, Volume 47
(1987).


<a id="biBwieser" name="biBwieser"></a>

[Wie78] Wieser, G.,
<a href="http://math.uni.lu/~wiese/notes/MFII.pdf">Computational arithmetic of modular forms </a>,
Universitat Duisburg-Essen 
(2007/8).


<a id="biBWustner" name="biBWustner"></a>

[Wue92] Wuestner, M.,
 An example of a nonsolvable Lie algebra
,
Seminar Sophus Lie 2, 57-58

(1992).


 

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