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Today's seminar
Seminar information archive ～12/04｜Today's seminar 12/05 | Future seminars 12/06～
2023/12/05
Tuesday Seminar on Topology
17:00-18:30 Room #ハイブリッド開催/056 (Graduate School of Math. Sci. Bldg.)
Pre-registration required. See our seminar webpage.
Teruaki Kitano (Soka University)
On the Euler class for flat S1-bundles, C∞ vs Cω (JAPANESE)
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
Pre-registration required. See our seminar webpage.
Teruaki Kitano (Soka University)
On the Euler class for flat S1-bundles, C∞ vs Cω (JAPANESE)
[ Abstract ]
We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S1 in terms of BΓ1 by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S1 bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.
[ Reference URL ]We describe low dimensional homology groups of the real analytic, orientation preserving diffeomorphism group of S1 in terms of BΓ1 by applying a theorem of Thurston. It is an open problem whether some power of the rational Euler class vanishes for real analytic flat S1 bundles. In this talk we discuss that if it does, then the homology group should contain many torsion classes that vanish in the smooth case. Along this line we can give a new proof for the non-triviality of any power of the rational Euler class in the smooth case. If time permits, we will mention some attempts to study a Mather-Thurston map in the analytic case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.
https://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index_e.html
