Morse-Bott Theory on posets and an homological Lusternik-Schnirelmann Theorem
D. Fern\'andez-Ternero, E. Mac\'ias-Virg\'os, D. Mosquera-Lois, J.A., Vilches
TL;DR
This paper extends Morse-Bott theory to posets and proves a Lusternik-Schnirelmann theorem for matchings on posets, broadening the theoretical framework for topological and combinatorial analysis.
Contribution
It introduces Morse-Bott theory on posets and establishes a Lusternik-Schnirelmann theorem for matchings, unifying discrete Morse-Bott theory and Morse theory on posets.
Findings
Developed Morse-Bott theory on posets.
Proved a Lusternik-Schnirelmann theorem for matchings on posets.
Unified concepts from discrete Morse-Bott theory and Morse theory.
Abstract
We develop Morse-Bott theory on posets, generalizing both discrete Morse-Bott theory for regular complexes and Morse theory on posets. Moreover, we prove a Lusternik-Schnirelmann theorem for general matchings on posets, in particular, for Morse-Bott functions.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models