The Euler characteristic of projectively flat manifolds with amenable fundamental groups

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...

The Euler characteristic of definable groups

We show that in an arbitrary o-minimal structure the following are equivalent: (i) every infinite, definably compact, definably connected definable group G has o-minimal Euler characteristic E(G) zero; (ii) if H is a definable subgroup of a definably compact, definably connected, definable group G such that E(G/H) 6= 0, then G = ∪{gHg−1 : g ∈ G}; (iii) every infinite, definably compact, definab...

Aspherical Manifolds with Relatively Hyperbolic Fundamental Groups

We show that the aspherical manifolds produced via the relative strict hyperbolization of polyhedra enjoy many group-theoretic and topological properties of open finite volume negatively pinched manifolds, including relative hyperbolicity, nonvanishing of simplicial volume, co-Hopf property, finiteness of outer automorphism group, absence of splitting over elementary subgroups, acylindricity, a...

74 the Deformation Spaces of Projectively Flat

Low dimensional flat manifolds with some classes of Finsler metric

Flat Riemannian manifolds are (up to isometry) quotient spaces of the Euclidean space R^n over a Bieberbach group and there are an exact classification of of them in 2 and 3 dimensions. In this paper, two classes of flat Finslerian manifolds are stuided and classified in dimensions 2 and 3.