トポロジー火曜セミナー

過去の記録 ~02/06次回の予定今後の予定 02/07~

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://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html
備考 Tea: 16:30 - 17:00 コモンルーム

2018年06月12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
三松 佳彦 氏 (中央大学)
Turbulization of 2-dimensional foliations on 4-manifolds (JAPANESE)
[ 講演概要 ]
This is a report on a joint work with Elmar VOGT(Freie Universität Berlin). For codimension 1 foliations, the process of turbulization, i.e., inserting a Reeb component along a closed transversal, is well-known, while for higher codimensional foliation, similar processes were not understood until around 2006.

In this talk, first we formulate the turbulization along a closed transversal. Then in our dimension setting, namely 2-dimensional foliations on 4-manifolds ((4,2)-foliations), a cohomological criterion is given for a given transversal to a foliation, which tells the turbulization is possible or not, relying on the Thurston's h-principle. Also we give cocrete geometric constructions of turbulizations.

The cohomological criterion for turbulization is deduced from a more general criterion for a given embedded surface to be a compact leaf or a closed transversal of some foliation, which is stated in terms of the euler classes of tangent and normal bndle of the foliation to look for. The anormalous cohomological solutions for certain cases suggested the geometric realization of turbulization, while the cohomological criterion is obtained by the h-principle.

Some other modifications are also formulated for (4,2)-foliations and their possibility are assured by the anormalous solutions mentioned above. For some of them, good geometric realizations are not yet known. So far the difficulty lies on the problem of the connected components of the space of representations of the surface groups to Diff S^1.

If the time permits, some special features on the h-principle for 2-dimensional foliations are also explained.