Infinite Analysis Seminar Tokyo

Date, time & place Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.)

2015/07/09

15:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Yuta Nozaki (Graduate School of Mathematical Sciences, the University of Tokyo) 15:00-16:30
An extension of the LMO functor and formal Gaussian integrals (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 certain Jacobi diagrams”.
In this talk, we extend the LMO functor to the case of any number of
boundary components.
In particular, we focus on a formal Gaussian integral, that is an
essential tool to construct the LMO functor.
Motoko Kato (Graduate School of Mathematical Sciences, the University of Tokyo) 17:00-18:30
On the relative number of ends of higher dimensional Thompson groups (JAPANESE)
[ Abstract ]
In 2004, Brin defined n−dimensional Thompson group nV for every natural number n ≥ 1. nV is a generalization of the Thompson group V . The Thompson group V can be described as a subgroup of the homeomorphism group of the Cantor set C. In this point of view, nV is a subgroup of the homeomorphism group of Cn. We prove that the number of ends of nV is equal to 1 and there is a subgroup of nV such that the relative number of ends is ∞. As a corollary of the second result, for each n, nV has Haagerup property and it can not be the fundamental group of a compact K ̈ahler manifold. These results are the generalizations of the corresponding results of Farley, who studied the Thompson group V .