Profinite rigidity and surface bundles over the circle
- 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- Not peer reviewed
- Copyright date:
- Pre-print available on arXiv.