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Tuesday Seminar on Topology
Seminar information archive ～05/17｜Next seminar｜Future seminars 05/18～
| Date, time & place | Tuesday 16:00 - 17:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | IKE Yuichi, KONNO Hokuto, SAKASAI Takuya |
2026/06/09
16:00-17:30 Room #hybrid/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Masato Tanabe (RIKEN iTHEMS)
Thom polynomials relative to maps prescribed near the boundary (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Masato Tanabe (RIKEN iTHEMS)
Thom polynomials relative to maps prescribed near the boundary (JAPANESE)
[ Abstract ]
Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In one important line of applications, various invariants of immersions have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, these results are obtained in different forms and remain somewhat scattered.
In this talk, I would like to present a relative version of Thom polynomial theory that places them in a unified framework. First, we introduce Thom polynomials relative to maps prescribed near the boundary, based on Steenrod's obstruction theory. Next, we show a structure theorem of Thom polynomials relative to framed immersions, using Kervaire's relative characteristic classes. Finally, we reinterpret earlier formulas within our framework, and also recover and generalize some of them, including Némethi--Pintér's formula for immersions associated with singular map-germs.
[ Reference URL ]Thom polynomials are universal cohomological obstructions to the appearance of singularities of given types in differentiable maps. Introduced by R. Thom in the 1950s, they have been extensively studied ever since. In one important line of applications, various invariants of immersions have been expressed in terms of singularities of their extensions (a.k.a. singular Seifert surfaces). However, these results are obtained in different forms and remain somewhat scattered.
In this talk, I would like to present a relative version of Thom polynomial theory that places them in a unified framework. First, we introduce Thom polynomials relative to maps prescribed near the boundary, based on Steenrod's obstruction theory. Next, we show a structure theorem of Thom polynomials relative to framed immersions, using Kervaire's relative characteristic classes. Finally, we reinterpret earlier formulas within our framework, and also recover and generalize some of them, including Némethi--Pintér's formula for immersions associated with singular map-germs.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
