Geometry & Topology, Vol. 1 (1997) Paper no. 3, pages 21-40.

Canonical decompositions of 3-manifolds

Walter D Neumann and Gadde A Swarup

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

AMS subject classification. Primary: 57N10, 57M99 Secondary: 57M35

DOI: 10.2140/gt.1997.1.21

E-print: arXiv:math.GT/9712227

Submitted to GT on February 2, 1997. Paper accepted July 30, 1997.

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Walter D Neumann and Gadde A Swarup
Department of Mathematics
The University of Melbourne
Parkville, Vic 3052
Australia
Email: neumann@ms.unimelb.edu.au and gadde@ms.unimelb.edu.au

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