Tuesday Seminar on Topology

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Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2015/07/07

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Takahiro Kitayama (Tokyo Institute of Technology)
Representation varieties detect essential surfaces (JAPANESE)
[ Abstract ]
Extending Culler-Shalen theory, Hara and I presented a way to construct
certain kinds of branched surfaces (possibly without any branch) 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 SL_2-theory. We show that every essential
surface in a 3-manifold is given by the ideal point of a line in the SL_
n-character variety for some n. The talk is partially based on joint
works with Stefan Friedl and Matthias Nagel, and also with Takashi Hara.