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Profinite rigidity and surface bundles over the circle

Accepted version
Peer-reviewed

Type

Article

Change log

Authors

Wilton, HJR 
Bridson, M 
Reid, A 

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 one of π1M and π1N maps onto G and the other does not.

Description

Keywords

math.GR, math.GR, math.GT, 20E18, 57M27, 20E26

Journal Title

Bulletin of the London Mathematical Society

Conference Name

Journal ISSN

0024-6093
1469-2120

Volume Title

Publisher

Wiley
Sponsorship
Engineering and Physical Sciences Research Council (EP/L026481/1)
The first author was supported in part by grants from the EPSRC and a Royal Society Wolfson Merit Award. The second author was supported in part by an NSF grant and The Wolfensohn Fund. He would also like to thank the Institute for Advanced Study for its hospitality whilst this work was completed. The third author was supported by a grant from the EPSRC.