Equivariant Algebraic Morse Theory
Ralf Donau
TL;DR
This paper extends Algebraic Morse Theory to situations where a group acts on a free chain complex, providing a new framework for analyzing symmetries in algebraic structures.
Contribution
It introduces an equivariant version of Algebraic Morse Theory, incorporating group actions into the existing framework for the first time.
Findings
Developed a formalism for group actions in Algebraic Morse Theory
Provided methods to simplify chain complexes with symmetries
Enhanced tools for studying algebraic structures with group actions
Abstract
In this paper we develop Algebraic Morse Theory for the case where a group acts on a free chain complex. Algebraic Morse Theory is an adaption of Discrete Morse Theory to free chain complexes.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology