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.