Diffeomorphism Groups

Department: 
MATH
Course Number: 
8803-BEL
Hours - Lecture: 
3
Hours - Total Credit: 
3

Outline: The course will cover algebraic and topological properties of diffeomorphism groups, which is a subject of current interest (e.g. it was a focus of three 2022 ICM talks). Topics will be selected from the following: diffeomorphism groups of surfaces and 3-manifolds, simplicity of diffeomorphism groups, maps between diffeomorphism groups, groups of volume-preserving diffeomorphisms, infinite-dimensional Lie groups, homotopy theory of diffeomorphisms groups of high-dimensional manifolds, such as disks and spheres.

Course Text: 

The monographs by Banyaga "The structure of classical diffeomorphism groups" and Kupers "Lectures on diffeomorphism groups of manifolds", as well as some research papers.