Immersed cycles and the JSJ decomposition

Suraj Krishna, Meda Satish

doi:10.2140/agt.2020.20.1877

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Immersed cycles and the JSJ decomposition

Suraj Krishna Meda Satish

Algebraic & Geometric Topology 20 (2020) 1877–1938

DOI: 10.2140/agt.2020.20.1877

Abstract

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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Keywords

CAT(0) square complexes, JSJ, cyclic splittings, isomorphism problem, graphs of free groups

Mathematical Subject Classification 2010

Primary: 20E06, 20E08, 20F65, 20F67

References

Publication

Received: 23 December 2018

Revised: 14 September 2019

Accepted: 15 November 2019

Published: 20 July 2020

Authors

Suraj Krishna Meda Satish
School of Mathematics Tata Institute of Fundamental Research Mumbai India

Volume 20, issue 4 (2020)