Geometry & Topology 12 (2008) 2537–2586

DOI: 10.2140/gt.2008.12.2537

Abstract

This is an expository article with complete proofs intended for a general nonspecialist audience. The results are two-fold. First, we discuss a geometric invariant, that we call the width, of a manifold and show how it can be realized as the sum of areas of minimal 2–spheres. For instance, when M is a homotopy 3–sphere, the width is loosely speaking the area of the smallest 2–sphere needed to ‘pull over’ M. Second, we use this to conclude that Hamilton’s Ricci flow becomes extinct in finite time on any homotopy 3–sphere.

Keywords

width, sweepout, min-max, Ricci flow, extinction, harmonic map, bubble convergence

Mathematical Subject Classification

Primary: 53C42, 53C44

Secondary: 58E12, 58E20

References

Publication

Received: 30 June 2007
Accepted: 10 October 2008
Published: 6 November 2008
Proposed: Ben Chow
Seconded: Colin Rourke, Martin Bridson

Authors