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Regular Neighbourhoods and Canonical Decompositions for Groups

Peter Scott·Gadde Swarup
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Abstract

We find canonical decompositions for finitely presented groups which specialize to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under automorphisms of the group. A crucial new ingredient is the concept of a regular neighbourhood for a finite family of almost invariant subsets of a group. An almost invariant set is an analogue of an immersion.

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Peter Scott, Gadde Swarup. 2001-12-20. Regular Neighbourhoods and Canonical Decompositions for Groups. https://arxiv.org/abs/math/0110210

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