Text only print
Full screen print
Tuesday Seminar on Topology
Seminar information archive ～04/22｜Next seminar｜Future seminars 04/23～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2019/11/19
17:00-18:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Ramón Barral Lijó (Ritsumeikan University)
The smooth Gromov space and the realization problem (ENGLISH)
Ramón Barral Lijó (Ritsumeikan University)
The smooth Gromov space and the realization problem (ENGLISH)
[ Abstract ]
The n-dimensional smooth Gromov space consists of the pointed isometry classes of complete Riemannian n-manifolds. In this talk we will present the definition and basic properties of this space as well as two different applications: The first addresses the following classical problem in foliation theory.
Realization problem: what kind of manifolds can be leaves of compact foliations?
Our joint work with Álvarez López has produced the following solution in the context of foliated spaces.
Theorem. Every Riemannian manifold of bounded geometry is a leaf in a compact foliated space X endowed with a metric tensor. Moreover, we can assume that X has trivial holonomy and is transversely Cantor.
The second application is the recent research by Abert and Biringer on the subject of unimodular random Riemannian manifolds.
The n-dimensional smooth Gromov space consists of the pointed isometry classes of complete Riemannian n-manifolds. In this talk we will present the definition and basic properties of this space as well as two different applications: The first addresses the following classical problem in foliation theory.
Realization problem: what kind of manifolds can be leaves of compact foliations?
Our joint work with Álvarez López has produced the following solution in the context of foliated spaces.
Theorem. Every Riemannian manifold of bounded geometry is a leaf in a compact foliated space X endowed with a metric tensor. Moreover, we can assume that X has trivial holonomy and is transversely Cantor.
The second application is the recent research by Abert and Biringer on the subject of unimodular random Riemannian manifolds.
