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Tuesday Seminar on Topology
Seminar information archive ～06/28｜Next seminar｜Future seminars 06/29～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | HABIRO Kazuo, KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2018/11/08
10:30-12:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Michael Heusener (Université Clermont Auvergne)
Deformations of diagonal representations of knot groups into SL(n,C) (ENGLISH)
Michael Heusener (Université Clermont Auvergne)
Deformations of diagonal representations of knot groups into SL(n,C) (ENGLISH)
[ Abstract ]
This is joint work with Leila Ben Abdelghani, Monastir (Tunisia).
Given a manifold M, the variety of representations of π1(M) into SL(2,C) and the variety of characters of such representations both contain information of the topology of M. Since the foundational work of W.P. Thurston and Culler & Shalen, the varieties of SL(2,C)-characters have been extensively studied. This is specially interesting for 3-dimensional manifolds, where the fundamental group and the geometrical properties of the manifold are strongly related.
However, much less is known of the character varieties for other groups, notably for SL(n,C) with n≥3. The SL(n,C)-character varieties for free groups have been studied by S. Lawton and P. Will, and the SL(3,C)-character variety of torus knot groups has been determined by V. Munoz and J. Porti.
In this talk I will present some results concerning the deformations of diagonal representations of knot groups in basic notations and some recent results concerning the representation and character varieties of 3-manifold groups and in particular knot groups. In particular, we are interested in the local structure of the SL(n,C)-representation variety at the diagonal representation.
This is joint work with Leila Ben Abdelghani, Monastir (Tunisia).
Given a manifold M, the variety of representations of π1(M) into SL(2,C) and the variety of characters of such representations both contain information of the topology of M. Since the foundational work of W.P. Thurston and Culler & Shalen, the varieties of SL(2,C)-characters have been extensively studied. This is specially interesting for 3-dimensional manifolds, where the fundamental group and the geometrical properties of the manifold are strongly related.
However, much less is known of the character varieties for other groups, notably for SL(n,C) with n≥3. The SL(n,C)-character varieties for free groups have been studied by S. Lawton and P. Will, and the SL(3,C)-character variety of torus knot groups has been determined by V. Munoz and J. Porti.
In this talk I will present some results concerning the deformations of diagonal representations of knot groups in basic notations and some recent results concerning the representation and character varieties of 3-manifold groups and in particular knot groups. In particular, we are interested in the local structure of the SL(n,C)-representation variety at the diagonal representation.
