SOME EXAMPLES OF T(6)-COMPLEXES AND HYPERBOLIC COMPLEXES

Abstract

The present thesis consists of three chapters. The first chapter covers basic material in geometric group theory, which make the theoretical base for our thesis. The second chapter gives some examples of2-complexes which satisfy the small cancellation condition T(6). In2.1 we give an example of T(6)-presentation (2-complex with a single vertex) which we call a positive T(6)-presentation and we give a way of combining positive T(6)-presentation to get new ones. In 2.2 we gtve further examples of T(6)-complexes called X-complexes such complexes whose star complexes are trisected. The third chapter covers hyperbolic complexes and we discuss the dependence. problem. There is an intimate connection between the dependence problem and diagrams on sphere and we gtve our main result which show that a necessary and sufficient condition for a non-orientable F-presentation to be hyperbolic.