[Binghamton Geometry/Topology Seminar] Michael Cohen (North Dakota State University)

[jwilliams at math.binghamton.edu]

Title: Polishability of some groups of interval and circle diffeomorphisms

Abstract:
Consider a group G consisting of all C^k diffeomorphisms of the circle
whose derivatives satisfy a regularity condition arising from classical
real analysis: a Lipschitz/Hoelder condition; absolute continuity; or
bounded total variation. Is it possible to assign a separable complete
metric topology to G, in such a way that the group operations become
continuous? If so, G is called Polishable. I'll discuss this Polishability
problem in the cases mentioned above, where the answer turns out to vary
dramatically depending on the choice of analytic condition. In particular,
I'll exhibit an infinite class of what appear to be new Polish topological
groups.

Thursday, Sept. 14, 2:50pm, WH-100E