On character of representations of flat hyperbolic bundle

Abstract

In this thesis, an invariant defined on the category of the hyperbolic flat bundle, called the character of a representation is discussed in for chapters. In chapter 2, some terminologies about flat bundles are defined briefly, and it is shown that two homotopic flat bundles are equivalent in the category of bundle. In chapter3, the invariant so-called "the character of a representation" is defined again by using the language of connection. In chapter 4, the main theorem of this thesis is proved: the invariant is stable on a component of a representaion variety.