Quantum cyclotomic orders of 3-manifolds

Details Quantum cyclotomic orders of 3-manifolds Quantum cyclotomic orders of 3-manifolds

1998-09-22

arxiv.org/abs/math/9809129v4

Topology 40 (2001) 95-125

Mathematics

Geometric Topology

Final version for publication (to appear in Topology). Only minor changes from the first posted version

Scientific paper

This paper provides a topological interpretation for number theoretic properties of quantum invariants of 3-manifolds. In particular, it is shown that the p-adic valuation of the quantum SO(3)-invariant of a 3-manifold M, for odd primes p, is bounded below by a linear function of the mod p first betti number of M. Sharper bounds using more delicate topological invariants related to Massey products are given as well.

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