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Analytic approach to $S^1$-equivariant M...
Zadeh, Mostafa E....

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Analytic approach to $S^1$-equivariant Morse inequalities by Zadeh, Mostafa E. ( Author )
Lemonjar Open Access
Australian National University
06-09-2023
It is well known that the cohomology groups of a closed manifold $M$ can be reconstructed using the gradient dynamical of a Morse-Smale function $f\colon M\to \R$. A direct result of this construction are Morse inequalities that provide lower bounds for the number of critical points of $f$ in term of Betti numbers of $M$. These inequalities can be deduced through a purely analytic method by studying the asymptotic behaviour of the deformed Laplacian operator. This method was introduced by E. Witten and has inspired a numbers of great achievements in Geometry and Topology in few past decades. In this paper, adopting the Witten approach, we provide an analytic proof for; the so called; equivariant Morse inequalities when the underlying manifold is acted on by the Lie group $G=S^1$ and the Morse function $f$ is invariant with respect to this action.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1411.7259
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