Canonical splittings of groups and 3-manifolds

2001/07/31 by Peter Scott, Gadde Swarup
Mathematics · #math.GT #math.GR #msc:57M07 #msc:57N10 #msc:20E06

paper · pdf

published as Trans. Amer. Math. Soc. 353 (2001), 4973-5001. · We have another paper in preparation which contains far more general algebraic results

arxiv created 2001/07/31 · arxiv updated 2009/11/30

Abstract

We introduce the notion of a `canonical' splitting over Z or ZxZ for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of M. This leads to a new proof of Johannson's Deformation Theorem.

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