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トポロジー火曜セミナー
過去の記録 ～05/17｜次回の予定｜今後の予定 05/18～
| 開催情報 | 火曜日 16:00～17:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 池 祐一, 今野 北斗, 逆井卓也 |
| セミナーURL | https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2026年06月09日(火)
16:00-17:30 数理科学研究科棟(駒場) hybrid/056号室
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
田邊 真郷 氏 (理化学研究所数理創造研究センター)
Thom polynomials relative to maps prescribed near the boundary (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
対面参加、オンライン参加のいずれの場合もセミナーのホームページから参加登録を行って下さい。
田邊 真郷 氏 (理化学研究所数理創造研究センター)
Thom polynomials relative to maps prescribed near the boundary (JAPANESE)
[ 講演概要 ]
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.
[ 参考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
