“ The Universal Functorial Lefschetz Invariant ” by Wolfgang Lück

The Universal Functorial Equivariant Lefschetz Invariant

We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K0 of the category of “φ-endomorphisms of finitely generated free RΠ(G,X)-modules”. We derive results about fixed points of equivariant endomorphisms of cocompact proper smooth G-manifolds.

The equivariant Lefschetz fixed point theorem for proper cocompact G-manifolds

Suppose one is given a discrete group G, a cocompact proper Gmanifold M , and a G-self-map f : M → M . Then we introduce the equivariant Lefschetz class of f , which is globally defined in terms of cellular chain complexes, and the local equivariant Lefschetz class of f , which is locally defined in terms of fixed point data. We prove the equivariant Lefschetz fixed point theorem, which says th...

Equivariant Lefschetz Maps for Simplicial Complexes and Smooth Manifolds

Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of Lefschetz numbers to equivariant K-homology classes. We compute the Lefschetz invariants for self-maps of finite-dimensional simplicial complexes and of self-maps o...

Reidemeister torsion and the K - theory of von Neumann algebras by Wolfgang Lück and Mel Rothenberg 0

The purpose of this paper is to introduce and study a new topological type invariant for cocompact properly discontinous actions of discrete groups of isometries on Riemannian manifolds. This work is inspired in part by the work of Carey and Mathai [4] and our invariant is a generalization of theirs. It is however much more refined and has the advantage of encompasing other powerful invariants ...

Equivariant homology theory and assembly maps by Wolfgang Lück ( Münster ) July 2006