Representation varieties detect splittings of 3-manifolds
SPEAKER | Takahiro Kitayama
DATE | May 10(Wed), 2017
TIME | 15:50
PLACE | 8101
ABSTRACT | Culler and Shalen established a method to construct nontrivial actions of a group on trees from ideal points of its SL_2-character variety. The method, in particular, gives essential surfaces in a 3-manifold corresponding to such actions of its fundamental group. Essential surfaces in some 3-manifold are known to be not detected in the classical SL_2-theory. We show that every essential surface in a 3-manifold is given by an ideal point of 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.