Local collapsing theory

F.T. Farrell and L.E. Jones

Vol. 210 (2003), No. 1, 1–100

DOI: 10.2140/pjm.2003.210.1

Abstract

The purpose of this paper is to introduce a variant of the geometric collapsing theory for Riemannian manifolds contained in the joint work of J. Cheeger, K. Fukaya and M. Gromov (henceforth called the “C-F-G-theory”). The authors make important use of this variant geometric collapsing theory in Farrell and Jones, 1998(2), to develop a theory for collapsing foliated Riemannian manifolds and then to prove topological rigidity for certain aspherical manifolds in Farrell and Jones, 1998(1).

Milestones

Received: 15 December 1997

Revised: 27 July 2000

Published: 1 May 2003