Morse Theory and Minimal Models

Abstract

In Chapter 6, we introduced the notion of 2-dimensional isoperimetric rank (6.32) as the largest number p, such that each simple curve of length ℓ is bounded by a disk of area at most Cℓ^p/p−1. This definition only makes sense in noncompact manifolds, and we have shown that the 2-dimensional isoperimetric rank of the universal cover of a compact manifold V depends only on the fundamental group π₁(V).