Polynomial-time proofs that groups are hyperbolic
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Date
05/2021Author
Grant ID
EP/I03582X/1
EP/I03582X/1
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It is undecidable in general whether a given finitely presented group is word hyperbolic. We use the concept of pregroups, introduced by Stallings (1971), to define a new class of van Kampen diagrams, which represent groups as quotients of virtually free groups. We then present a polynomial-time procedure that analyses these diagrams, and either returns an explicit linear Dehn function for the presentation, or returns fail, together with its reasons for failure. Furthermore, if our procedure succeeds we are often able to produce in polynomial time a word problem solver for the presentation that runs in linear time. Our algorithms have been implemented, and when successful they are many orders of magnitude faster than KBMAG, the only comparable publicly available software.
Citation
Holt , D , Linton , S , Neunhoeffer , M , Parker , R , Pfeiffer , M & Roney-Dougal , C M 2021 , ' Polynomial-time proofs that groups are hyperbolic ' , Journal of Symbolic Computation , vol. 104 , pp. 419-475 . https://doi.org/10.1016/j.jsc.2020.08.003
Publication
Journal of Symbolic Computation
Status
Peer reviewed
ISSN
0747-7171Type
Journal article
Description
Funding: UK EPSRC grant number EP/I03582X/1.Collections
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