Volume 1, issue 1 (1997)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Canonical decompositions of 3–manifolds

Walter D Neumann and Gadde A Swarup

Geometry & Topology 1 (1997) 21–40

arXiv: math.GT/9712227

Abstract

We describe a new approach to the canonical decompositions of 3–manifolds along tori and annuli due to Jaco–Shalen and Johannson (with ideas from Waldhausen) – the so-called JSJ–decomposition theorem. This approach gives an accessible proof of the decomposition theorem; in particular it does not use the annulus–torus theorems, and the theory of Seifert fibrations does not need to be developed in advance.

Keywords
3–manifold, torus decomposition, JSJ–decomposition, Seifert manifold, simple manifold
Mathematical Subject Classification
Primary: 57N10, 57M99
Secondary: 57M35
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Publication
Received: 25 February 1997
Accepted: 27 July 1997
Published: 30 July 1997
Proposed: David Gabai
Seconded: Robion Kirby, Ronald Stern
Authors
Walter D Neumann
Department of Mathematics
The University of Melbourne
Parkville
Victoria 3052
Australia
Gadde A Swarup
Department of Mathematics
The University of Melbourne
Parkville
Victoria 3052
Australia