The holomorphic Lefschetz formula
نویسندگان
چکیده
منابع مشابه
CALCULATIONS OF THE HIRZEBRUCH χy GENERA OF SYMMETRIC PRODUCTS BY THE HOLOMORPHIC LEFSCHETZ FORMULA
We calculate the Hirzebruch χy andˆχy-genera of symmetric products of closed complex manifolds by the holomorphic Lefschetz formula of Atiyah and Singer [4]. Such calculation rederive some formulas proved in an earlier paper [14] by a different method. Let M be a smooth manifold, and G a finite group of diffeomorphisms. There are two kinds of interesting cohomology theories for the orbifold M/G...
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We caution that # Fix(ψ) has to be interpreted with some care: it really denotes a fixed point count with multiplicities. A better way to phrase it as follows. Inside M ×M we have two submanifolds: the diagonal ∆ and the graph Γψ. We can then try to take # Fix(ψ) := ∆ · Γψ = “intersection number of ∆ and Γψ”. When ∆ and Γψ intersect transversely this intersection number coincides with the naïve...
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We want to formulate an analogous statement for a flow Φ instead of a diffeomorphism. By looking at the local side of (1) the first idea would be to consider the fixed points of the flow and to assume they are nondegenerate. This way we get the Hopf formula expressing the Euler characteristic on the global side. More subtle information is supposed to be obtained by considering the closed orbits...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1975
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1975-13954-1