Integrality of the Averaged Jones Polynomial of Algebraically Split
- Additional Document Info
- View All
X.-S. Lin and Z. Wang recently made a conjecture concerning the integrality
of the Taylor coefficients of the averaged Jones polynomial of algebraically
split links. This question is related to a conjectural integrality result for
the Ohtsuki invariants, which are rational topological invariants of homology
3-spheres derived from the quantum invariants of Witten and Reshetikhin-Turaev.
This paper presents counterexamples to the conjecture of Lin and Wang and
gives a proof of a corrected statement of the conjecture. The statement is
divided into two parts. The first part applies to geometrically split links and
gives an integrality result which is stronger than conjectured, while the
second is valid for any algebraically split link and gives a somewhat weaker
statement. Both propositions are seen to be sharp by the examples given.