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Regular neighbourhoods and canonical decompositions for groups. (English) Zbl 1057.20032

Summary: We find canonical decompositions for finitely presented groups which essentially specialise 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 of a family of almost invariant subsets of a group. An almost invariant set is an analogue of an immersion.

MSC:

20F65 Geometric group theory
20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations
20F05 Generators, relations, and presentations of groups
57M05 Fundamental group, presentations, free differential calculus
57M07 Topological methods in group theory
57Q40 Regular neighborhoods in PL-topology
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References:

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