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Tuesday Seminar on Topology
Seminar information archive ～04/26｜Next seminar｜Future seminars 04/27～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2016/12/13
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Mitsumatsu (Chuo University)
Plane fields on 3-manifolds and asymptotic linking of the tangential incompressible flows (JAPANESE)
Yoshihiko Mitsumatsu (Chuo University)
Plane fields on 3-manifolds and asymptotic linking of the tangential incompressible flows (JAPANESE)
[ Abstract ]
This is a report on a project in (a very slow) progress which aims to prove the tightness of contact structures associated with algebraic Anosov flows without using Bennequin's nor Gromov's results.
After introducing an interpretation of asymptotic linking pairing in terms of differential forms, we attach a subspaces of exact 2-forms to each plane field. We analyze this space in the case where the plane field is an algebraic Anosov foliation and explain what can be done using results from foliated cohomology and frameworks for secondary characteristic classes. We also show some explicit computations.
To close the talk, a quantization phenomenon which happens when a foliation is deformed into a contact structure is explained and we state some perspectives on applying the results on foliations to the tightness.
This is a report on a project in (a very slow) progress which aims to prove the tightness of contact structures associated with algebraic Anosov flows without using Bennequin's nor Gromov's results.
After introducing an interpretation of asymptotic linking pairing in terms of differential forms, we attach a subspaces of exact 2-forms to each plane field. We analyze this space in the case where the plane field is an algebraic Anosov foliation and explain what can be done using results from foliated cohomology and frameworks for secondary characteristic classes. We also show some explicit computations.
To close the talk, a quantization phenomenon which happens when a foliation is deformed into a contact structure is explained and we state some perspectives on applying the results on foliations to the tightness.
