Holomorphic Lefschetz formula for manifolds with boundary
- The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M-->M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschetz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah- Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschetz formula on a strictly convex domain in C-n, n>1
Author details: | Alexander M. Kytmanov, Simona Myslivets, Nikolai Nikolaevich TarkhanovORCiDGND |
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ISSN: | 0025-5874 |
Publication type: | Article |
Language: | English |
Year of first publication: | 2004 |
Publication year: | 2004 |
Release date: | 2017/03/24 |
Source: | Mathematische Zeitschrift. - ISSN 0025-5874. - 246 (2004), 4, S. 769 - 794 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
Peer review: | Referiert |