Vol. 73, No. 1, 1977

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Dehn’s construction and the Poincaré conjecture

Norris Freeman Weaver

Vol. 73 (1977), No. 1, 247–255
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
Authors
Norris Freeman Weaver