Invariants and Bestvina-Brady Groups

ABSTRACT: The aim of this thesis is to compute the Euler Characteristic of the Bestvina-Brady groups. First, the analytical topology, the point-set topology is introduced. Then, the main purpose of the use of algebraic topology; the homeomorphism problem is stated. To understand the homeomorphism problem, certain well-known topological spaces are defined, and to solve it, the notion of topological invariants is introduced. Two main topological invariants; Euler characteristic and the Fundamental group theories are studied. Finally, by the use of C.T.C. Wall and the Bestvina-Brady papers, under certain homotopic conditions the Euler Characteristic of the Bestvina-Brady groups is computed. Keywords: Topological invariants, Euler Characteristic, Fundamental Group, Bestvina - Brady Group. …………………………………………………………………………………………………………………………