Lefschetz numbers for sheaf-trivial proper surjections

A characterization of sheaf-trivial, proper maps with cohomologically locally connected images

Let f : X-, Y be a proper surjection of locally compact metric spaces. Throughout, the Leray sheafs of f are assumed to be (locally) trivial either in all dimensions or through a given dimension. Using a spectral sequence, the cohomological local connectivity of Y is analyzed and thus characterized by the structure of f. We define f to be cohomologically locally connected if, for each y E Y, ne...

On partitions, surjections, and Stirling numbers

On the Relative Dualising Sheaf of a Symplectic Lefschetz Fibration

For the dualising sheaf ωX/B of a relatively minimal symplectic Lefschetz fibration π : X → B, we show that c21(ωX/B) ≥ 0. Some consequences related to the Hodge bundle are obtained.

Periods for Holomorphic Maps via Lefschetz Numbers

In this note we are concerned with fixed point theory for holomorphic self maps on complex manifolds. After the well-known Schwarz lemma on the unit disk, which assumes a fixed point, the Pick theorem was proved in [8]. This can be extended to a Pick-type theorem on hyperbolic Riemann surfaces as is shown in [5, 7]. For a more general type of space: open, connected and bounded subsets of a Bana...

Transversality and Lefschetz Numbers for Foliation Maps

Let F be a smooth foliation on a closed Riemannian manifold M , and let Λ be a transverse invariant measure of F . Suppose that Λ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then a topological definition of the Λ-Lefschetz number of any leaf preserving diffeomorphism (M,F) → (M,F) is given. For this purpose, standard results about smooth approximation a...