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Tuesday Seminar on Topology
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| 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 |
2017/12/12
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Tatsuro Shimizu (RIMS, Kyoto university)
On the self-intersection of singular sets of maps and the signature defect (JAPANESE)
Tatsuro Shimizu (RIMS, Kyoto university)
On the self-intersection of singular sets of maps and the signature defect (JAPANESE)
[ Abstract ]
Let $M$ be a closed oriented $n$-dimensional manifold. We give a geometric proof of that the $k$-times self-intersection of singular set of a Morin map from $M$ to $R^p$ coincides with the corank $k$ singular set of any generic map from $M$ to $R^{p+k-1}$ as homology classes with $Z/2$ coefficient ($n>p+k-2$). As an application we give a description of the signature defect of framed 3-manifold from the point of view of singular sets of maps.
Let $M$ be a closed oriented $n$-dimensional manifold. We give a geometric proof of that the $k$-times self-intersection of singular set of a Morin map from $M$ to $R^p$ coincides with the corank $k$ singular set of any generic map from $M$ to $R^{p+k-1}$ as homology classes with $Z/2$ coefficient ($n>p+k-2$). As an application we give a description of the signature defect of framed 3-manifold from the point of view of singular sets of maps.
