Mapping degree and Euler characteristic

Exponentiation and Euler Characteristic

The Euler Characteristic

I will describe a few basic properties of the Euler characteristic and then I use them to prove special case of a cute formula due to Bernstein-Khovanskii-Koushnirenko. 1. Basic properties of the Euler characteristic The Euler characteristic is a function χ which associates to each reasonable topological space X an integer χ(X). For us a reasonable space would be a space which admits a finite s...

ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS

In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...

On Curvature and Euler-poincare Characteristic.

Secondary Characteristic Classes and the Euler Class

We discuss secondary (and higher) characteristic classes for algebraic vector bundles with trivial top Chern class. We then show that if X is a smooth affine scheme of dimension d over a field k of finite 2cohomological dimension (with char(k) 6= 2) and E is a rank d vector bundle over X , vanishing of the Chow-Witt theoretic Euler class of E is equivalent to vanishing of its top Chern class an...