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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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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Name:
Royal Society
Funding agency for:
Bridson, M
More from this funder
Name:
Engineering and Physicals Sciences Research Council
Funding agency for:
Bridson, M
Publication date:
2016-10-01
Keywords:
Pubs id:
pubs:518838
UUID:
uuid:d4293386-4c53-48d5-9fd1-74b956f6a503
Local pid:
pubs:518838
Source identifiers:
518838
Deposit date:
2016-10-20

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