Sang-hyun KIM

Title:
Diffeomorphism Groups of One-Manifolds

Abstract:
Let M be a compact interval or a circle. We study algebraic properties of Diff^r(M), the group of C^r diffeomorphisms of M. In the first half of the minicourse, we investigate r=0 (homeomorphisms), particularly on the cohomological aspects.
For the second half, we focus on the following question: which finitely generated groups arise as subgroups of Diff^r(M)? After surveying classical theories of Hölder, Denjoy, Kopell and Thurston, we prove (a joint work with Thomas Koberda) 
that such ``finitely generated subgroup spectra'' are different for all distinct real numbers r, s >=2.