Representation varieties detect essential surfaces

2016/04/03 by Friedl, Stefan, Kitayama, Takahiro, Nagel, Matthias
#20E42 (Secondary) #57M05 #57N10 (Primary) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1604.00584

Abstract

Extending Culler-Shalen theory, Hara and the second author presented a way to construct certain kinds of branched surfaces in a 3-manifold from an ideal point of a curve in the SL_n-character variety. There exists an essential surface in some 3-manifold known to be not detected in the classical SL₂-theory. We prove that every connected essential surface in a 3-manifold is given by an ideal point of a rational curve in the SL_n-character variety for some n.

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