Filling invariants: homological vs. homotopical

Abstract

Classical isoperimetric functions give optimal bounds on the minimal-area fillings of loops by disks. There are a number of variations: rather than sticking to loops and disks, one might consider fillings of spheres by balls, or cycles by chains. A natural question then is: for a given space are these functions the same? Or are there spaces in which a particular type of filling (say filling cycles by chains) is more efficient than other types? What if the space is quasi-isometric to a finitely presented group? I will talk about recent work with A. Abrams, N. Brady and R. Young which addresses this question.