Geometry & Topology 1 (1997) 21–40

DOI: 10.2140/gt.1997.1.21

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: 57M99, 57N10

Secondary: 57M35

References

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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