Abstract
Given an invariant of a knot , the corresponding 1–tangle invariant is defined as the quotient of by its value on the unknot . We prove here that when is the Homfly satellite invariant determined by decorating with any eigenvector of the meridian map in the Homfly skein of the annulus then is always an integer 2–variable Laurent polynomial. Specialisation of the 2–variable polynomials for suitable choices of eigenvector shows that the 1–tangle irreducible quantum invariants of are integer 1–variable Laurent polynomials.
Citation
H R Morton. "Integrality of Homfly 1–tangle invariants." Algebr. Geom. Topol. 7 (1) 327 - 338, 2007. https://doi.org/10.2140/agt.2007.7.327
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