Dehn’s construction and the Poincaré conjecture

Norris Freeman Weaver

Vol. 73 (1977), No. 1, 247–255

DOI: 10.2140/pjm.1977.73.247

Abstract

M. Dehn used a type of homology preserving surgery on S³ to produce an infinite family of irreducible homology 3-spheres. We apply Dehn’s construction to arbitrary 3-manifolds, give groups invariant under Dehn’s construction, give a reduction of the Poincaré conjecture, give a nontrivial example of links in S³ with homeomorphic exteriors, and give a result connerning knots with property P.

Mathematical Subject Classification

Primary: 55A99, 55A99

Secondary: 57A10

Milestones

Received: 7 June 1977

Published: 1 November 1977