トポロジー火曜セミナー

過去の記録 ~04/29次回の予定今後の予定 04/30~

開催情報 火曜日 17:00~18:30 数理科学研究科棟(駒場) 056号室
担当者 河野 俊丈, 河澄 響矢, 北山 貴裕, 逆井卓也
セミナーURL http://faculty.ms.u-tokyo.ac.jp/~topology/index.html
備考 Tea: 16:30 - 17:00 コモンルーム

2017年05月09日(火)

17:00-18:30   数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
諏訪 立雄 氏 (北海道大学)
Local and global coincidence homology classes (JAPANESE)
[ 講演概要 ]
We consider two differentiable maps between two oriented manifolds. In the case the manifolds are compact with the same dimension and the coincidence points are isolated, there is the Lefschetz coincidence point formula, which generalizes his fixed point formula. In this talk we discuss the case where the dimensions of the manifolds may possible be different so that the coincidence points are not isolated in general. In fact it seems that Lefschetz himself already considered this case (cf. [4]).

We introduce the local and global coincidence homology classes and state a general coincidence point theorem.
We then give some explicit expressions for the local class. We also take up the case of several maps as considered in [1] and perform similar tasks. These all together lead to a generalization of the aforementioned Lefschetz formula. The key ingredients are the Alexander duality in combinatorial topology, intersection theory with maps and the Thom class in Čech-de Rham cohomology. The contents of the talk are in [2] and [3].

References
[1] C. Biasi, A.K.M. Libardi and T.F.M. Monis, The Lefschetz coincidence class of p maps, Forum Math. 27 (2015), 1717-1728.
[2] C. Bisi, F. Bracci, T. Izawa and T. Suwa, Localized intersection of currents and the Lefschetz coincidence point theorem, Annali di Mat. Pura ed Applicata 195 (2016), 601-621.
[3] J.-P. Brasselet and T. Suwa, Local and global coincidence homology classes, arXiv:1612.02105.
[4] N.E. Steenrod, The work and influence of Professor Lefschetz in algebraic topology, Algebraic Geometry and Topology: A Symposium in Honor of Solomon Lefschetz, Princeton Univ. Press 1957, 24-43.