Related papers: The universal Euler characteristic for varieties o…

To an arbitrary variety over a field of characteristic zero, we associate a complex of Chow motives, which is, up to homotopy, unique and bounded. We deduce that any variety has a natural Euler characteristic in the Grothendieck group of…

It is well known that the Euler characteristic of an odd dimensional compact manifold is zero. An Euler complex is a combinatorial analogue of a compact manifold. We present here an elementary proof of the corresponding result for Euler…

The Euler characteristic was defined for finite strict n-categories by Leinster using the theory of enriched categories. This was an extension of some of his earlier work, which defined Euler characteristic for finite categories. Building…

We discuss the universal orbifold Euler characteristic and generalized orbifold Euler characteristics corresponding to finitely generated groups $A$ (the $A$-Euler characteristics). We show that the collection of all $A$-Euler…

The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…

We propose a definition of an Euler characteristic for unbounded chain complexes by taking the (usual) Euler characteristics of successively longer parts of the complex, weighted inversely proportional to the length, and passing to the…

We study Grothedieck groups of triangulated categories using weight structures, weight complexes, and the corresponding pure (co)homological functors. We prove some general statements on $K_0$ of weighted categories and apply it to…

The notion of the orbifold Euler characteristic came from physics at the end of 80's. There were defined higher order versions of the orbifold Euler characteristic and generalized ("motivic") versions of them. In a previous paper the…

We discuss Euler characteristics for finitely generated modules over Iwasawa algebras. We show that the Euler characteristic of a module is well-defined whenever the 0th homology group is finite if and only if the relevant compact p-adic…

The paper studies weak Paley-Wiener properties for group extensions by use of Mackey's theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem…

Complete proofs of Schur-Weyl duality in positive characteristic are scarce in the literature. The purpose of this survey is to write out the details of such a proof, deriving the result in positive characteristic from the classical result…

This note studies the behavior of Euler characteristics and of intersection homology Euler characterstics under proper morphisms of algebraic (or analytic) varieties. The methods also yield, for algebraic (or analytic) varieties, formulae…

We define Euler characteristic of a category enriched by a monoidal model category. If a monoidal model category V is equipped with Euler characteristic that is compatible with weak equivalences and fibrations in V, then our Euler…

We explore some of the special features with respect to Bredon cohomology of groups having all its finite subgroups either nilpotent or p-groups or cyclic p-groups. We get some results on dimensions and also a formula for the equivariant…

We consider the problem of computing the Euler characteristic of an abstract simplicial complex given by its vertices and facets. We show that this problem is #P-complete and present two new practical algorithms for computing Euler…

The Euler characteristic of a semialgebraic set can be considered as a generalization of the cardinality of a finite set. An advantage of semialgebraic sets is that we can define "negative sets" to be the sets with negative Euler…

Generating functions for the number of commuting m-tuples in the symmetric groups are obtained. We define a natural sequence of ``orbifold Euler characteristics'' for a finite group G acting on a manifold X. Our definition generalizes the…

In this note we show that Waldhausen's K-theory functor from Waldhausen categories to spaces has a universal property: It is the target of the "universal global Euler characteristic", in other words, the "additivization" of the functor…

Every absolutely summing linear operator is weakly compact. However, for strongly summing multilinear operators and polynomials - one of the most natural extensions of the linear case to the non linear framework - weak compactness does not…

Let $G$ be a $(2,m,n)$-group and let $x$ be the number of distinct primes dividing $\chi$, the Euler characteristic of $G$. We prove, first, that, apart from a finite number of known exceptions, a non-abelian simple composition factor $T$…