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Infinite Analysis Seminar Tokyo
Seminar information archive ～04/19｜Next seminar｜Future seminars 04/20～
| Date, time & place | Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|
2015/02/19
13:30-17:00 Room #002 (Graduate School of Math. Sci. Bldg.)
Shunsuke Tsuji (Graduate School of Mathematical Sciences, the University of Tokyo) 13:30-15:00
Skein algebra and mapping class group (JAPANESE)
An extension of the LMO functor (JAPANESE)
Shunsuke Tsuji (Graduate School of Mathematical Sciences, the University of Tokyo) 13:30-15:00
Skein algebra and mapping class group (JAPANESE)
[ Abstract ]
We define some filtrations of skein modules and the skein algebra on an oriented surface, and define the completed skein modules and
the completed skein algebra of the surface with respect to these filtration. We give an explicit formula for the action of the Dehn
twists on the completed skein modules in terms of the action of the completed skein algebra of the surface. As an application, we describe the action of the Johnson kernel on the completed skein modules.
Yuta Nozaki (Graduate School of Mathematical Sciences, the University of Tokyo) 15:30-17:00We define some filtrations of skein modules and the skein algebra on an oriented surface, and define the completed skein modules and
the completed skein algebra of the surface with respect to these filtration. We give an explicit formula for the action of the Dehn
twists on the completed skein modules in terms of the action of the completed skein algebra of the surface. As an application, we describe the action of the Johnson kernel on the completed skein modules.
An extension of the LMO functor (JAPANESE)
[ Abstract ]
Cheptea, Habiro and Massuyeau introduced the LMO functor as an extension of the LMO invariant of closed 3-manifolds. The LMO functor is “the monoidal category of Lagrangian cobordisms between surfaces with at most one boundary component” to “the monoidal category of top-substantial Jacobi diagrams”. In this talk, we extend the LMO functor to the case of any number of boundary components. Moreover, we explain that the internal degree d part of the extension is a finite-type invariant of degree d.
Cheptea, Habiro and Massuyeau introduced the LMO functor as an extension of the LMO invariant of closed 3-manifolds. The LMO functor is “the monoidal category of Lagrangian cobordisms between surfaces with at most one boundary component” to “the monoidal category of top-substantial Jacobi diagrams”. In this talk, we extend the LMO functor to the case of any number of boundary components. Moreover, we explain that the internal degree d part of the extension is a finite-type invariant of degree d.
