Boolean complexes of involutions
Combinatorics
2021-09-14 v1
Abstract
Let (W,S) be a Coxeter system. We introduce the boolean complex of involutions of W which is an analogue of the boolean complex of W studied by Ragnarsson and Tenner. By applying discrete Morse theory, we determine the homotopy type of the boolean complex of involutions for a large class of (W,S), including all finite Coxeter groups, finding that the homotopy type is that of a wedge of spheres of dimension |S| - 1. In addition, we find simple recurrence formulas for the number of spheres in the wedge.
Keywords
Cite
@article{arxiv.2109.05832,
title = {Boolean complexes of involutions},
author = {Axel Hultman and Vincent Umutabazi},
journal= {arXiv preprint arXiv:2109.05832},
year = {2021}
}
Comments
17 pages, 6 figures