Ricci flow with surgery on three-manifolds

TL;DR

This paper develops a Ricci flow with surgery on three-manifolds, verifying most of the previous claims, and advances the understanding of Ricci flow techniques in geometric topology.

Contribution

It constructs and verifies Ricci flow with surgeries on three-manifolds, addressing previous assertions and refining the understanding of manifold collapse and volume bounds.

Findings

Constructed Ricci flow with surgeries on three-manifolds

Verified most assertions from previous work

Refined understanding of volume bounds and collapse scenarios

Abstract

This is a technical paper, which is a continuation of math.DG/0211159. Here we construct Ricci flow with surgeries and verify most of the assertions, made in section 13 of that e-print; the exceptions are (1) the statement that manifolds that can collapse with local lower bound on sectional curvature are graph manifolds - this is deferred to a separate paper, since the proof has nothing to do with the Ricci flow, and (2) the claim on the lower bound for the volume of maximal horns and the smoothness of solutions from some time on, which turned out to be unjustified and, on the other hand, irrelevant for the other conclusions.