Text only print
Full screen print
Tuesday Seminar on Topology
Seminar information archive ～04/16｜Next seminar｜Future seminars 04/17～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2010/01/12
16:30-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
篠原 克寿 (東京大学大学院数理科学研究科) 16:30-17:30
Index problem for generically-wild homoclinic classes in dimension three
On a generalized suspension theorem for directed Fukaya categories
篠原 克寿 (東京大学大学院数理科学研究科) 16:30-17:30
Index problem for generically-wild homoclinic classes in dimension three
[ Abstract ]
In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.
二木 昌宏 (東京大学大学院数理科学研究科) 17:30-18:30In the sphere of non-hyperbolic differentiable dynamical systems, one can construct an example of a homolinic class which does not admit any kind of dominated splittings (a weak form of hyperbolicity) in a robust way. In this talk, we discuss the index (dimension of the unstable manifold) of the periodic points inside such homoclinic classes from a $C^1$-generic viewpoint.
On a generalized suspension theorem for directed Fukaya categories
[ Abstract ]
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to
\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.
Recently Seidel has proved that this is stable under the suspension $W
+ u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'
\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.
The directed Fukaya category $\\mathrm{Fuk} W$ of exact Lefschetz
fibration $W : X \\to \\mathbb{C}$ proposed by Kontsevich is a
categorification of the Milnor lattice of $W$. This is defined as the
directed $A_\\infty$-category $\\mathrm{Fuk} W = \\mathrm{Fuk}^\\to
\\mathbb{V}$ generated by a distinguished basis $\\mathbb{V}$ of
vanishing cycles.
Recently Seidel has proved that this is stable under the suspension $W
+ u^2$ as a consequence of his foundational work on the directed
Fukaya category. We generalize his suspension theorem to the $W + u^d$
case by considering partial tensor product $\\mathrm{Fuk} W \\otimes'
\\mathcal{A}_{d-1}$, where $\\mathcal{A}_{d-1}$ is the category
corresponding to the $A_n$-type quiver. This also generalizes a recent
work by the author with Kazushi Ueda.
