Homotopy types of group lattices
I.P. Kramarev, L.V. Lokutsievskiy
TL;DR
This paper investigates the topological properties of group lattices, specifically their homotopy types, and explores their connections and Betti number estimates using spectral sequences.
Contribution
It determines the homotopy type of the subgroup lattice of PSL(2,7), links different group lattices, and estimates Betti numbers with spectral sequences.
Findings
Homotopy type of PSL(2,7) subgroup lattice identified
Connections established between various group lattices
Betti number estimates obtained using spectral sequences
Abstract
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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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Algebra and Logic