Morse theory for loop-free categories
Algebraic Topology
2021-07-14 v1
Abstract
We extend discrete Morse-Bott theory to the setting of loop-free (or acyclic) categories. First of all, we state a homological version of Quillen's Theorem A in this context and introduce the notion of cellular categories. Second, we present a notion of vector field for loop-free categories. Third, we prove a homological collapsing theorem in the absence of critical objects in order to obtain the Morse inequalities. Examples are provided through the exposition. This answers partially a question by T. John: whether there is a Morse theory for loop-free (or acyclic) categories? [14].
Cite
@article{arxiv.2107.06202,
title = {Morse theory for loop-free categories},
author = {Michał Lipiński and David Mosquera-Lois and Mateusz Przybylski},
journal= {arXiv preprint arXiv:2107.06202},
year = {2021}
}