A Lefschetz fixed point formula for elliptic differential operators

A Lefschetz Fixed Point Formula for Elliptic Differential Operators

Introduction. The classical Lefschetz fixed point formula expresses, under suitable circumstances, the number of fixed points of a continuous map ƒ : X-+X in terms of the transformation induced by ƒ on the cohomology of X. If X is not just a topological space but has some further structure, and if this structure is preserved by ƒ, one would expect to be able to refine the Lefschetz formula and ...

Lefschetz Fixed Point Formula for Manifolds with Cylindrical Ends

Supersymmtric Quantum Mechanics and Lefschetz fixed-point formula

We review the explicit derivation of the Gauss-Bonet and Hirzebruch formulae by physical model and give a physical proof of the Lefschetz fixed-point formula by twisting boundary conditions for the path integral.

The Lefschetz Fixed Point Theorem

The Lefschetz Fixed Point Theorem generalizes a collection of fixed point theorems for different topological spaces, including maps on the n-sphere and the n-disk. Although the theorem is easily written in terms of compact manifolds, in this paper we will work entirely with topological spaces that are simplicial complexes or retracts of simplicial complexes. After developing the fundamentals of...

A Lefschetz Fixed Point Formula for Singular Arithmetic Schemes with Smooth Generic Fibres

In this article, we consider singular equivariant arithmetic schemes whose generic fibres are smooth. For such schemes, we prove a relative fixed point formula of Lefschetz type in the context of Arakelov geometry. This formula is an analog, in the arithmetic case, of the Lefschetz formula proved by R. W. Thomason in [31]. In particular, our result implies a fixed point formula which was conjec...