Witten deformation for noncompact manifolds with bounded geometry
| Autor: | Xianzhe Dai, Junrong Yan |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Instanton General Mathematics media_common.quotation_subject FOS: Physical sciences Geometry Mathematical Physics (math-ph) Mathematics::Spectral Theory Infinity Mathematics::Algebraic Topology Manifold Cohomology Mathematics - Analysis of PDEs Differential Geometry (math.DG) Bounded function FOS: Mathematics Laplace operator Mathematics::Symplectic Geometry Mathematical Physics Eigenvalues and eigenvectors Morse theory media_common Mathematics Analysis of PDEs (math.AP) |
| ISSN: | 1474-7480 |
| DOI: | 10.48550/arxiv.2005.04607 |
| Popis: | Motivated by the Landau–Ginzburg model, we study the Witten deformation on a noncompact manifold with bounded geometry, together with some tameness condition on the growth of the Morse function f near infinity. We prove that the cohomology of the Witten deformation $d_{Tf}$ acting on the complex of smooth $L^2$ forms is isomorphic to the cohomology of the Thom–Smale complex of f as well as the relative cohomology of a certain pair $(M, U)$ for sufficiently large T. We establish an Agmon estimate for eigenforms of the Witten Laplacian which plays an essential role in identifying these cohomologies via Witten’s instanton complex, defined in terms of eigenspaces of the Witten Laplacian for small eigenvalues. As an application, we obtain the strong Morse inequalities in this setting. |
| Databáze: | OpenAIRE |
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