2023 / December Volume 18 No.4
Semi-classical heat kernel asymptotics and Morse inequalities
Published Date |
2023 / December
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Title | Semi-classical heat kernel asymptotics and Morse inequalities |
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Pagination | 365-418 |
Abstract | In this paper, we study the asymptotic behavior of the heat kernel with respect to the Witten Laplacian. We introduce the localization and the scaling technique in semi-classical analysis, and study the semi-classical asymptotic behavior of the family of the heat kernel, indexed by $k$, near the critical point $p$ of a given Morse function, as $k\to \infty$. It is shown that this family is approximately close to the heat kernel with respect to a system of the harmonic oscillators attached to $p$. We also furnish some asymptotic results regarding heat kernels away from the critical points. These heat kernel asymptotic results lead to a novel proof of the Morse inequalities. |
DOI | |
AMS Subject Classification |
58J35
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Received |
2023-11-30
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