Mathematical software

The program Bianchi.gp belongs to the PLUME index of the CNRS.
Bianchi.gp computes a fundamental domain for the Bianchi groups in hyperbolic 3-space, the associated quotient space and essential information about the group homology and equivariant K-homology of the Bianchi groups.
Bianchi.gp is part of the GP Scripts Library of PARI/GP Development Center. The intensive computations award C3I has been attributed to the thesis developing Bianchi.gp.
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The Torsion Subcomplexes Subpackage (joint work with Tuan Anh Bui) in HAP is a GAP sub-package for Torsion Subcomplex Reduction to be applied to cell complexes with an action of a discrete group. The paper The Farrell--Tate and Bredon homology for PSL_4(Z) and other arithmetic groups (joint work with Tuan Anh Bui and Matthias Wendt) explains the Rigid Facets Subdivision algorithm, which is the main new feature in the current version (2.0) of the subpackage.
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The Davis Complex package in HAP, by Alexander D. Rahm and Ruben J. Sanchez-Garcia, is a GAP sub-package which creates a combinatorial model of the Davis complex of an arbitrary Coxeter group. The Davis complex has been defined in [M.W. Davis, Groups generated by reflections, Ann. Math. 117 (1983)]; and the present sub-package is a release of the implementation described in [R.J. Sanchez-Garcia, Equivariant K-homology for some Coxeter groups, J. London Math. Soc. (2) 75 (2007)].


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