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Profinite rigidity and surface bundles over the circle

Abstract:
If M is a compact 3-manifold whose first betti number is 1, and N is a compact 3-manifold such that π1N and π1M have the same finite quotients, then M fibres over the circle if and only if N does. We prove that groups of the form F2⋊Z are distinguished from one another by their profinite completions. Thus, regardless of betti number, if M and N are punctured torus bundles over the circle and M is not homeomorphic to N, then there is a finite group G such that π1M maps onto G and π1N does not.
Publication status:
Not published
Peer review status:
Not peer reviewed

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Institution:
University of Oxford
Oxford college:
Magdalen College
Role:
Author
Journal:
arXiv Journal website
Publication date:
2016-10-07
Source identifiers:
653442
Keywords:
Pubs id:
pubs:653442
UUID:
uuid:c31997a4-116a-43fb-99bd-784379c1f988
Local pid:
pubs:653442
Deposit date:
2017-01-06

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