We prove an equivariant Grothendieck-Ogg-Shafarevich formula. This formula may be viewed as an étale analogue of well-known formulas for Zariski sheaves which were proved by Ellingsrud/Lønsted and Nakajima and for which we give a new approach in this paper. Mathematics Subject Classification 2000. 14F20; 14L30; 14H30.

We prove that any real-analytic, volume-preserving action of a lattice Γ in a simple Lie group with Q-rank(Γ) ≥ 7 on a closed 4-manifold of nonzero Euler characteristic factors through a finite group action.

We study moduli spaces of vector bundles on a two dimensional neighborhood Zk of an irreducible curve C ' P with C = −k and give an explicit construction of these moduli as stratified spaces. We give sharp bounds for the local Euler characteristic of bundles on Zk and prove existence of families of bundles with prescribed numerical invariants.

It is well known that every polyhedral map with large enough number of vertices contains a vertex of degree at most 6. In this paper the existence of stars having low degree sum of their vertices in polyhedral maps is investigated. We will prove: if G is a polyhedral map on compact 2-manifold M with non-positive Euler characteristic (M) and G has more than 149| (M)| vertices then G contains an ...

If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the manifold and its boundary. So essentially, Euler characteristic is the unique invariant of this type.

Given a compact connected component of zeros of a vector field, we give a necessary condition for its asymptotic stability in terms of its index and Euler characteristic.

The object of this paper is to develop and prove an equivariant Grothendieck-OggShafarevich formula. Let k be an algebraically closed field, X a connected smooth projective curve over k and G a finite subgroup of Aut(X/k) of order n. Furthermore, let l 6= char(k) be a prime and F a constructible Fl-sheaf on the étale site Xét which carries a G-action compatible with the given G-action on X. The...

We prove that that the number p of positive eigenvalues of the connection Laplacian L of a finite abstract simplicial complex G matches the number b of even dimensional simplices in G and that the number n of negative eigenvalues matches the number f of odd-dimensional simplices in G. The Euler characteristic X(G) of G therefore can be spectrally described as X(G)=p-n. This is in contrast to th...

The Getzler’s formula relates the Sn-equivariant Hodge-Deligne polynomial of the space of ordered tuples of distinct points on a given variety X with the Hodge-Deligne polynomial of X. We obtain the analogue of this formula for the case when X has a nontrivial automorphism group. Collecting together all strata of M2 with different automorphism groups, we derive a formula for the Sn-equivariant ...

The idea of enumeration using the Euler characteristic was suggested throughout Rota’s work and influenced by Schanuel’s categorical viewpoint [33, 40, 41, 42]. In order to carry out such a program that is topologically meaningful and which captures the broadest possible classes of examples, two key insights are required. First, the notion of grading in the face lattice of a polytope must be re...