Geometry and Geometric Analysis Working Group
Some topological isoperimetric problems
Speaker: Fedor Manin, Ohio State University
Location: Warren Weaver Hall 517
Date: Monday, November 12, 2018, 11 a.m.
I will discuss the following questions (due mostly to Gromov) and some partial answers:
- Given a nullcobordant manifold of (uniformly) bounded geometry and volume \(V\), how does the minimal volume of a nullcobordism of bounded geometry depend on \(V\)?
- Given compact metric spaces \(X\) and \(Y\) and a nullhomotopic \(L\)-Lipschitz map \(f:X \to Y\), how does the minimal Lipschitz constant of a nullhomotopy depend on \(L\)?
Both of these can be seen as a kind of isoperimetric question, and are closely related to each other as well as to more classical notions of isoperimetry.