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arXiv · 1810.04248

The homotopy type of skeleta of the flag complex over a finite vector space

Jorge Aguilar-Guzman·Jesus Gonzalez·Jose Luis Leon-Medina
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Abstract

The aim of this paper is to give a (discrete) Morse theoretic proof of the fact that the $k$-th skeleton of the flag complex $\mathcal{F}$, associated to the lattice of subspaces of a finite dimensional vector space, is homotopy equivalent to a wedge of spheres of dimension $\min\{k,\dim(\mathcal{F})\}$. The tight control provided by Morse theoretic methods allows us to give an explicit formula for the number of spheres appearing in each of these wedge summands.

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Jorge Aguilar-Guzman, Jesus Gonzalez, Jose Luis Leon-Medina. 2018-10-09. The homotopy type of skeleta of the flag complex over a finite vector space. https://arxiv.org/abs/1810.04248

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