- FIELD
- Math:Topology
- DATE
- May 14 (Tue), 2024
- TIME
- 14:00 ~ 15:30
- PLACE
- 1423
- SPEAKER
- Nariman, Sam
- HOST
- Kim, Sang-hyun
- INSTITUTE
- Purdue University
- TITLE
- The bounded cohomology of transformation groups of Euclidean spaces and discs
- ABSTRACT
- In-person and Zoom hybrid https://visgat.kimsh.kr May 13, 2024 (Mon), 3 - 4 pm, KIAS 1503, "Groupoids, diffeomorphisms, and invariants of foliations" May 14, 2024 (Tue), 11 - 12 pm, KIAS 1423, "The bounded cohomology of transformation groups of Euclidean spaces and discs" Talk 1: Groupoids, diffeomorphisms, and invariants of foliations In this talk, we will discuss the equivariant version of Mather-Thurston’s theorem that relates the group cohomology of diffeomorphism groups to the classifying space of the groupoid of germs. I will explain two applications of this perspective. One is about PL homeomorphisms of surfaces. We discuss that Greenberg's work on PL foliations can be used to answer the case of surfaces of a question posed by Epstein in 1970 about the simplicity of PL homeomorphisms that are isotopic to the identity., I will talk about another application for invariants of flat sphere bundles which answers a question posed by Haefliger. For example, we will see that for G a finite-dimensional connected Lie group, any principal G-bundle over a closed manifold is cobordant via $G$-bundles to a foliated G-bundle (not necessarily flat principal G-bundle). Talk 2: The bounded cohomology of transformation groups of Euclidean spaces and discs In this talk, I will first talk about a joint work with N. Monod about a method to calculate the bounded cohomology of the diffeomorphism group of spheres. Then I will report on a work in progress with Francesco Fournier-Facio and Nicolas Monod on the bounded cohomology of Homeo(R^n) and Homeo(D^n).
- FILE