On Hempel Pairs and Turaev-Viro Invariants

Abstract

Surface bundles arising from periodic mapping classes may sometimes have non-isomorphic, but profinitely isomorphic fundamental groups. Pairs of this kind have been discovered by Hempel. This paper exhibits examples of nontrivial Hempel pairs where the mapping tori can be distinguished by some Turaev-Viro invariants, and also examples where they cannot be distinguished by any Turaev-Viro invariants.

Keywords

Profinite completion / Mapping class group / Turaev-Viro invariant / 57K31 / 57K16

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