Volume 20, issue 4 (2020)

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Immersed cycles and the JSJ decomposition

Suraj Krishna Meda Satish

Algebraic & Geometric Topology 20 (2020) 1877–1938

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.

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CAT(0) square complexes, JSJ, cyclic splittings, isomorphism problem, graphs of free groups
Mathematical Subject Classification 2010
Primary: 20E06, 20E08, 20F65, 20F67
Received: 23 December 2018
Revised: 14 September 2019
Accepted: 15 November 2019
Published: 20 July 2020
Suraj Krishna Meda Satish
School of Mathematics
Tata Institute of Fundamental Research