Wythoff polytopes and low-dimensional homology of Mathieu groups

2008/12/22 by Mathieu Dutour Sikirić, Mathieu Dutour Sikiric, Sikiric, Mathieu Dutour +2 · 1 citation
Chemistry · Mathematics · #Axial and Atropisomeric Chirality Synthesis #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.0812.4291

10 pages, 1 figure, 4 tables

arxiv created 2009/09/01 · arxiv updated 2009/12/01

Abstract

We describe two methods for computing the low-dimensional integral homology of the Mathieu simple groups and use them to make computations such as H₅(M₂₃,\ZZ)=\ZZ₇ and H₃(M₂₄,\ZZ)=\ZZ₁₂. One method works via Sylow subgroups. The other method uses a Wythoff polytope and perturbation techniques to produce an explicit free \ZZ M_n-resolution. Both methods apply in principle to arbitrary finite groups.

Cited by

• An Invitation to Computational Homotopy

Related

• An algorithm for low dimensional group homology
• Low-dimensional Homology of SL₂(k[t,1/t])
• Rational K3 Homotopy and the Largest Mathieu Group
• A polytope combinatorics for semisimple groups
• Homology of Gaussian groups