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The complexity of balanced presentations and the Andrews-Curtis conjecture

Abstract:

Motivated by problems in topology, we explore the complexity of balanced group presentations. We obtain large lower bounds on the complexity of Andrews-Curtis trivialisations, beginning in rank 4. Our results are based on a new understanding of how Dehn functions of groups behave under certain kinds of push-outs.


We consider groups S with presentations of deficiency 1 satisfying certain technical conditions and construct balanced group presentations Pw indexed by words w in th...

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Publication status:
Submitted
Peer review status:
Under review

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Department:
Oxford, MPLS, Mathematical Institute
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Funding agency for:
Bridson, MR
Publication date:
2016-10-05
Pubs id:
pubs:518838
URN:
uri:d4293386-4c53-48d5-9fd1-74b956f6a503
UUID:
uuid:d4293386-4c53-48d5-9fd1-74b956f6a503
Local pid:
pubs:518838

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