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The relative cup-length in local Morse cohomology

Year: 2024

Type: article

Abstract: Local Morse cohomology associates cohomology groups to isolating neighbourhoods of gradient flows of Morse functions on (generally non-compact) Riemannian manifolds $M$. We show that local Morse cohomology is a module over the cohomology of the isolating neighbourhood, which allows us to define a cup-length relative to the cohomology of the isolating neighbourhood that gives a lower bound on the number of critical points of functions on $M$ that are not necessarily Morse. Finally, we illustrate by an example that this lower bound can indeed be stronger than the lower bound given by the absolute cup-length.

Source: Topological Methods in Nonlinear Analysis

DOI: 10.12775/tmna.2024.002

Authors: Thomas Rot, Maciej Starostka, Nils Waterstraat

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4402781969

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