FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 5, PAGES 103-123

Homotopy types of group lattices

I. P. Kramarev
L. V. Lokutsievskiy

Abstract

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In this article, we study group lattices using the ideas by K. S. Brown and D. Quillen of associating a certain topological space to a partially ordered set. We determine the exact homotopy type for the subgroup lattice of $PSL(2,7)$, find a connection between different group lattices, and obtain some estimates for the Betty numbers of these lattices using the spectral sequence method.

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Last modified: May 7, 2009