Canonical splittings of groups and 3-manifolds

Peter Scott; Gadde Swarup

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Canonical splittings of groups and 3-manifolds

Peter Scott·Gadde Swarup

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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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Peter Scott, Gadde Swarup. 2001-07-31. Canonical splittings of groups and 3-manifolds. https://arxiv.org/abs/math/0107232

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