Morse homology of manifolds with boundary revisited
Manabu Akaho
TL;DR
This paper revisits Morse homology for manifolds with boundary, providing detailed insights into its structure through handlebody decompositions, enhancing understanding of topological invariants in such manifolds.
Contribution
It offers a detailed re-examination of Morse homology on manifolds with boundary, connecting it explicitly to handlebody decompositions for clearer topological interpretation.
Findings
Clarifies the relationship between Morse homology and handlebody decompositions.
Provides detailed proofs and constructions for manifolds with boundary.
Enhances the theoretical framework for Morse homology in boundary cases.
Abstract
This re-certifying paper describes the details of the Morse homology of manifolds with boundary, introduced by the author before, in terms of handlebody decompositions.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis