Тип публикации: статья из журнала
Год издания: 2004
Идентификатор DOI: 10.1070/SM2004v195n12ABEH000865
Аннотация: The classical Lefschetz 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 obtained a holomorphic Lefschetz formula on cПоказать полностьюompact complex manifolds without boundary. Brenner and Shubin (1981, 1991) extended the Atiyah-Bott theory to compact manifolds with boundary. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, therefore the Atiyah-Bott theory is not applicable. Bypassing difficulties related to the boundary behaviour of Dolbeault cohomology, Donnelly and Fefferman (1986) obtained a formula for the number of fixed points in terms of the Bergman metric. The aim of this paper is to obtain a Lefschetz formula on relatively compact strictly pseudoconvex subdomains of complex manifolds X with smooth boundary, that is, to find the total Lefschetz number for a holomorphic endomorphism f(*) of the Dolbeault complex and to express it in terms of local invariants of the fixed points of f.
Журнал: SBORNIK MATHEMATICS
Выпуск журнала: Vol. 195, Is. 11-12
Номера страниц: 1757-1779
ISSN журнала: 10645616
Место издания: LETCHWORTH
Издатель: LONDON MATHEMATICAL SOCIETY RUSSIAN ACAD SCIENCES