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Tuesday Seminar on Topology
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2017/07/04
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Jean-Baptiste Meilhan (Université Grenoble Alpes)
On link-homotopy for knotted surfaces in 4-space (ENGLISH)
Jean-Baptiste Meilhan (Université Grenoble Alpes)
On link-homotopy for knotted surfaces in 4-space (ENGLISH)
[ Abstract ]
The purpose of this talk is to show how combinatorial objects (welded objects, which is a natural quotient of virtual knot theory) can be used to study knotted surfaces in 4-space.
We will first consider the case of 'ribbon' knotted surfaces, which are embedded surfaces bounding immersed 3-manifolds with only ribbon singularities. More precisely, we will consider ribbon knotted annuli ; these objects act naturally on the reduced free group, and we prove, using welded theory, that this action gives a classification up to link-homotopy, that is, up to continuous deformations leaving distinct component disjoint. This in turns implies a classification result for ribbon knotted tori.
Next, we will show how to extend this classification result beyond the ribbon case.
This is based on joint works with B. Audoux, P. Bellingeri and E. Wagner.
The purpose of this talk is to show how combinatorial objects (welded objects, which is a natural quotient of virtual knot theory) can be used to study knotted surfaces in 4-space.
We will first consider the case of 'ribbon' knotted surfaces, which are embedded surfaces bounding immersed 3-manifolds with only ribbon singularities. More precisely, we will consider ribbon knotted annuli ; these objects act naturally on the reduced free group, and we prove, using welded theory, that this action gives a classification up to link-homotopy, that is, up to continuous deformations leaving distinct component disjoint. This in turns implies a classification result for ribbon knotted tori.
Next, we will show how to extend this classification result beyond the ribbon case.
This is based on joint works with B. Audoux, P. Bellingeri and E. Wagner.
