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Tuesday Seminar on Topology
Seminar information archive ～01/20｜Next seminar｜Future seminars 01/21～
| 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 |
2026/01/21
16:00-17:00 Room #hybrid/118 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
Understanding the well-rounded deformation retraction of Teichmüller space (ENGLISH)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Ingrid Irmer (Southern University of Science and Technology)
Understanding the well-rounded deformation retraction of Teichmüller space (ENGLISH)
[ Abstract ]
The term "well-rounded deformation retraction" goes back to a paper of Ash in which equivariant deformation retractions of the space of $n\times n$ positive-definite real symmetric matrices acted on by $SL(n,\mathbb{Z})$ were studied. An informal analogy between families of groups, such as $SL(n,\mathbb{Z})$, $Out(F_{n})$ and mapping class groups, suggests the existence of a similar equivariant deformation retractions of the actions of $Out(F_{n})$ and mapping class groups on well-chosen spaces. In all these examples, there are spaces on which the respective groups act with known equivariant deformation retractions onto cell complexes of the smallest possible dimension --- the virtual cohomological dimension of the group. The purpose of this talk is to explain that the equivariant deformation retraction of the action of the mapping class group on Teichmüller space can be understood to be a piecewise-smooth analogue of Ash's well rounded deformation retraction. The key idea is to understand the role of duality in correctly drawing this analogy.
[ Reference URL ]The term "well-rounded deformation retraction" goes back to a paper of Ash in which equivariant deformation retractions of the space of $n\times n$ positive-definite real symmetric matrices acted on by $SL(n,\mathbb{Z})$ were studied. An informal analogy between families of groups, such as $SL(n,\mathbb{Z})$, $Out(F_{n})$ and mapping class groups, suggests the existence of a similar equivariant deformation retractions of the actions of $Out(F_{n})$ and mapping class groups on well-chosen spaces. In all these examples, there are spaces on which the respective groups act with known equivariant deformation retractions onto cell complexes of the smallest possible dimension --- the virtual cohomological dimension of the group. The purpose of this talk is to explain that the equivariant deformation retraction of the action of the mapping class group on Teichmüller space can be understood to be a piecewise-smooth analogue of Ash's well rounded deformation retraction. The key idea is to understand the role of duality in correctly drawing this analogy.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
