相关论文: Coincidence invariants and higher Reidemeister tra…

The Lefschetz fixed point theorem follows easily from the identification of the Lefschetz number with the fixed point index. This identification is a consequence of the functoriality of the trace in symmetric monoidal categories. There are…

By the Lefschetz fixed point theorem, if an endomorphism of a topological space is fixed-point-free, then its Lefschetz number vanishes. This necessary condition is not usually sufficient, however; for that we need a refinement of the…

The Lefschetz fixed point theorem and its converse have many generalizations. One of these generalizations is to endomorphisms of a space relative to a fixed subspace. In this paper we define relative Lefschetz numbers and Reidemeister…

We reexamine equivariant generalizations of the Lefschetz number and Reidemeister trace using categorical traces. This gives simple, conceptual descriptions of the invariants as well as direct comparisons to previously defined…

We prove two general decomposition theorems for fixed-point invariants: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar additivity results for these invariants. Moreover, the proofs of…

In topological fixed point theory, the Reidemeister trace is an invariant associated to a selfmap of a polyhedron which combines information from the Lefschetz and Nielsen numbers. In this paper we define the Reidemeister trace in the…

In the setting of continuous maps between compact orientable manifolds of the same dimension, there is a well known averaging formula for the coincidence Lefschetz number in terms of the Lefschetz numbers of lifts to some finite covering…

We give a homotopy invariant construction of the Reidemeister trace for the coincidence of two maps between closed manifolds of not necessarily the same dimensions. It is realized as a homology class of the homotopy equalizer, which…

We introduce a theory of integration with respect to the fixed point index, offering a substantial improvement over previous approaches based on the Lefschetz number. This framework eliminates several restrictive assumptions -- such as the…

The fixed point index of topological fixed point theory is a well studied integer-valued algebraic invariant of a mapping which can be characterized by a small set of axioms. The coincidence index is an extension of the concept to…

We show that the combinatorial Lefschetz number is a topological invariant. This is an important result in itself; in order to point it out, we will also work here several relevant consequences in different directions. The first of them is…

We show that an important classical fixed point invariant, the Reidemeister trace, arises as a topological Hochschild homology transfer. This generalizes a corresponding classical result for the Euler characteristic and is a first step in…

We show that in any symmetric monoidal category, if a weight for colimits is absolute, then the resulting colimit of any diagram of dualizable objects is again dualizable. Moreover, in this case, if an endomorphism of the colimit is induced…

Let $F$ be a smooth foliation on a closed Riemannian manifold $M$, and let $\Lambda$ be a transverse invariant measure of $F$. Suppose that $\Lambda$ is absolutely continuous with respect to the Lebesgue measure on smooth transversals. Then…

Traces in symmetric monoidal categories are well-known and have many applications; for instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for some applications, such as generalizations of the…

We describe generators of universal Lefschetz groups consisting of self-maps of equivariant 1-spheres. This allows to formulate a normalization axiom which, together with the usual axioms, determines an equivariant Lefschetz number…

We prove two general factorization theorems for fixed-point invariants of fibrations: one for the Lefschetz number and one for the Reidemeister trace. These theorems imply the familiar multiplicativity results for the Lefschetz and Nielsen…

We compute the trace of an endomorphism in equivariant bivariant K-theory for a compact group G in several ways: geometrically using geometric correspondences, algebraically using localisation, and as a Hattori-Stallings trace. This results…

In this paper, we present two types of Lefschetz numbers in the topology of digital images. Namely, the simplicial Lefschetz number $L(f)$ and the cubical Lefschetz number $\bar L(f)$. We show that $L(f)$ is a strong homotopy invariant and…

We give axioms which characterize the local Reidemeister trace for orientable differentiable manifolds. The local Reidemeister trace in fixed point theory is already known, and we provide both uniqueness and existence results for the local…