Euler characteristic on noncommutative polyballs

On Curvature and Euler-poincare 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 Euler characteristic of definable groups

We show that in an arbitrary o-minimal structure the following are equivalent: (i) conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; (ii) every infinite, definably connected, definably compact definable group has a non trivial torsion point. ∗The author was supported b...

On Euler Characteristic of Equivariant Sheaves

Let k be an algebraically closed field of characteristic p > 0 and let l be another prime number. O. Gabber and F. Loeser proved that for any algebraic torus T over k and any perverse l-adic sheaf F on T the Euler characteristic χ(F) is non-negative. We conjecture that the same result holds for any perverse sheaf F on a reductive group G over k which is equivariant with respect to the adjoint a...