Morse-Smale flow, Milnor metric, and dynamical zeta function
| Autor: | Shu Shen, Jianqing Yu |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Closed manifold General Mathematics Dynamical Systems (math.DS) Absolute value (algebra) Fixed point Cohomology Riemann zeta function symbols.namesake Differential Geometry (math.DG) Flow (mathematics) Mathematics::K-Theory and Homology Flat vector bundle Metric (mathematics) FOS: Mathematics symbols Mathematics - Dynamical Systems Mathematics |
| Zdroj: | Journal de l’École polytechnique — Mathématiques. 8:585-607 |
| ISSN: | 2270-518X |
| Popis: | We introduce a Milnor metric on the determinant line of the cohomology of the underlying closed manifold with coefficients in a flat vector bundle, by means of interactions between the fixed points and the closed orbits of a Morse-Smale flow. This allows us to generalise the notion of the absolute value at zero point of the Ruelle dynamical zeta function, even in the case where this value is not well defined in the classical sense. We give a formula relating the Milnor metric and the Ray-Singer metric. An essential ingredient of our proof is Bismut-Zhang's Theorem. Final version |
| Databáze: | OpenAIRE |
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