Matching and Independence Complexes Related to Small Grids

2016/06/03 by Braun, Benjamin, Hough, Wesley K. · 1 citation
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1606.01204

Abstract

The topology of the matching complex for the 2× n grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes Ind(Δ_n^m) that include these matching complexes. Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain Ind(Δ_n^m). Further, we determine the Euler characteristic of Ind(Δ_n^m) and prove that several homology groups of Ind(Δ_n^m) are non-zero.

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• Independence Complexes of Hexagonal Grid Graphs

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