Skein theory and Witten-Reshetikhin-Turaev Invariants of links in lens spaces

Patrick M. Gilmer

doi:10.1007/s002200050588

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arXiv · math/9801132

Skein theory and Witten-Reshetikhin-Turaev Invariants of links in lens spaces

Patrick M. Gilmer

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Abstract

We study the behavior of the Witten-Reshetikhin-Turaev SU(2) invariants of links in L(p,q) as a function of the level r-2. They are given by 1 over the square root of r times one of p Laurent polynomials evaluated at e to the 2 pi i divided by 4pr. The congruence class of r modulo p determines which polynomial is applicable. If p is zero modulo four, the meridian of L(p,q) is non-trivial in the skein module but has trivial Witten-Reshetikhin-Turaev SU(2) invariants. On the other hand, we show that one may recover the element in the Kauffman bracket skein module of L(p,q) represented by a link from the collection of the WRT invariants at all levels if p is a prime or twice an odd prime. By a more delicate argument, this is also shown to be true for p=9.

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BibTeX RIS

Patrick M. Gilmer. 1998-01-28. Skein theory and Witten-Reshetikhin-Turaev Invariants of links in lens spaces. https://doi.org/10.1007/s002200050588

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