Equivariant Morse inequalities and applications
Wen Lu
TL;DR
This paper establishes equivariant Morse inequalities using analytic localization techniques and applies these results to derive Morse inequalities on compact manifolds with boundary.
Contribution
It introduces a novel proof of equivariant Morse inequalities employing Bismut-Lebeau's localization, extending their application to manifolds with boundary.
Findings
Proved equivariant Morse inequalities using localization techniques
Extended Morse inequalities to manifolds with boundary
Demonstrated applications to doubling manifolds
Abstract
In this paper, we prove equivariant Morse inequalities via Bismut-Lebeau's analytic localization techniques. As an application, we obtain Morse inequalities on compact manifold with nonempty boundary by applying equivariant Morse inequalities to the doubling manifold.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Geometric Analysis and Curvature Flows