Immersed cycles and the JSJ decomposition

Suraj Krishna, Meda Satish¹

¹School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India

Algebraic and Geometric Topology, Tome 20 (2020) no. 4, pp. 1877-1938

Résumé

We present an algorithm to construct the JSJ decomposition of one-ended hyperbolic groups which are fundamental groups of graphs of free groups with cyclic edge groups. Our algorithm runs in double exponential time and is the first algorithm on JSJ decompositions to have an explicit time bound. Our methods are combinatorial/geometric and rely on analysing properties of immersed cycles in certain CAT(0) square complexes.

Détail

DOI : 10.2140/agt.2020.20.1877

Classification : 20E06, 20E08, 20F65, 20F67
Keywords: CAT(0) square complexes, JSJ, cyclic splittings, isomorphism problem, graphs of free groups

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