Canonical splittings of groups and 3-manifolds

Scott, Peter; Swarup, Gadde

doi:10.1090/S0002-9947-01-02871-9

Canonical splittings of groups and 3-manifolds
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by Peter Scott and Gadde A. Swarup PDF

Trans. Amer. Math. Soc. 353 (2001), 4973-5001 Request permission

Abstract:

We introduce the notion of a ‘canonical’ splitting over $\mathbb {Z}$ or $\mathbb {Z}\times \mathbb {Z}$ 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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