The relative cup-length in local Morse cohomology

Thomas O. Rot; Maciej Starostka; Nils Waterstraat

doi:10.12775/tmna.2024.002

The relative cup-length in local Morse cohomology

Abstract

Local Morse cohomology associates cohomology groups to isolating neighborhoods 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 neighborhood, which allows us to define a cup-length relative to the cohomology of the isolating neighborhood 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.

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Keywords

MORSE COHOMOLOGY, CUP-PRODUCT, CRITICAL POINTS

Details

Category:

Articles

Type:

artykuły w czasopismach dostępnych w wersji elektronicznej [także online]

Published in:

Topological Methods in Nonlinear Analysis pages 1 - 15,
ISSN: 1230-3429

Language:

English

Publication year:

2024

Bibliographic description:

Rot T. O., Starostka M., Waterstraat N., The relative cup-length in local Morse cohomology, Topological Methods in Nonlinear Analysis, 2024,10.12775/TMNA.2024.002

DOI: