Discrete Morse Theory and a Reformulation of the K(\pi,1)-conjecture
Algebraic Topology
2013-09-17 v2 Group Theory
Abstract
A recent theorem of Dobrinskaya states that the K(\pi,1)-conjecture holds for an Artin group G if and only if the canonical map from BM to BG is a homotopy equivalence, where M denotes the Artin monoid associated to G. The aim of this paper is to give an alternative proof by means of discrete Morse theory and abstract homotopy theory. Moreover, we exhibit a new model for the classifying space of an Artin monoid, in the spirit of Charney, Meier and Whittlesey, and a small chain complex for computing its monoid homology, similar to the one of Squier.
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Cite
@article{arxiv.1309.1337,
title = {Discrete Morse Theory and a Reformulation of the K(\pi,1)-conjecture},
author = {Viktoriya Ozornova},
journal= {arXiv preprint arXiv:1309.1337},
year = {2013}
}
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