Character varieties of higher dimensional representations and splittings of 3-manifolds

Abstract

In 1983 Culler and Shalen established a way to construct essential surfaces in a 3-manifold from ideal points of the $S{L}_2$-character variety associated to the 3-manifold group. We present in this article an analogous construction of certain kinds of branched surfaces (which we call essential tribranched surfaces) from ideal points of the $S{L}_n$-character variety for a natural number $n$ greater than or equal to 3. Further we verify that such a branched surface induces a nontrivial presentation of the 3-manifold group in terms of the fundamental group of a certain 2-dimensional complex of groups.

33 pages and 10 figures. We have added to the latest version other figures (Figures 4 and 5) and Lemma 4.7, which states that the inverse image of Y(K) under a piecewisely-linear map is indeed a tribranched surface contained in M

References in corpus (2)

• Graph manifolds with boundary are virtually special
• Local coordinates for SL(n,C) character varieties of finite volume hyperbolic 3-manifolds