Reducibility and Anosov Representations

Abstract:

In this thesis, we explore the framework of Anosov representations for reducible representations of a non-elementary word hyperbolic group. We give characterizations of the Anosov condition for these reducible representations in terms of the eigenvalues of the irreducible block factors of its semisimplification, or more generally, of the block factors of its block diagonalization. In the character variety, these Anosov representations comprise a collection of bounded convex domains in certain finite-dimensional vector spaces, and this perspective allows us to conclude for many non-elementary hyperbolic groups that connected components of the character variety which consist entirely of Anosov representations do not contain reducible representations. Applying these results to reducible suspensions, we obtain explicit examples of non-Anosov limits of reducible Anosov representations.