By gluing together copies of an all-right angled Coxeter polytope a number of open hyperbolic 6-manifolds with Euler characteristic −1 are constructed. They are the first known examples of hyperbolic 6-manifolds having the smallest possible volume.

We give a formula for the Sn-equivariant Euler characteristics of the moduli spaces Mg,n of genus g curves with n marked points.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper we introduce the generalized twisted q-Euler numbers E (α) Keywords: Euler numbers and polynomials, twisted q-Euler numbers and q-Euler polynomials, generalized twisted q-Euler numbers and polynomials, q-Euler ze...

We introduce notions of finiteness obstruction, Euler characteristic, L2-Euler characteristic, and Möbius inversion for wide classes of categories. The finiteness obstruction of a category Γ of type (FP) is a class in the projective class group K0(RΓ); the Euler characteristic and L2-Euler characteristic are respectively its RΓ-rank and L2-rank. We also extend the second author’s K-theoretic Mö...