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

2014/10/16 by Hara, Takashi, Kitayama, Takahiro
#20E42 (secondary) #57M27 (primary) #57Q10 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1410.4295

Abstract

In 1983 Culler and Shalen established a way to construct essential surfaces in a 3-manifold from ideal points of the SL₂-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 SL_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.

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