Canonical splittings of groups and 3-manifolds

Details Canonical splittings of groups and 3-manifolds Canonical splittings of groups and 3-manifolds

2001-07-31

arxiv.org/abs/math/0107232v1

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

Mathematics

Geometric Topology

We have another paper in preparation which contains far more general algebraic results

Scientific paper

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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