A contribution of a U(1)-reducible connection to quantum invariants of links II: Links in rational homology spheres

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dc.creatorRozansky, L.
dc.date1998-06-11
dc.date1999-06-06
dc.date.accessioned2026-07-07T05:25:01Z
dc.date.available2026-07-07T05:25:01Z
dc.descriptionWe extend the definition of the U(1)-reducible connection contribution to the case of the Witten-Reshetikhin-Turaev invariant of a link in a rational homology sphere. We prove that, similarly ot the case of a link in S^3, this contribution is a formal power series in powers of q-1, whose coefficients are rational functions of q^{color}, their denominators being the powers of the Alexander-Conway polynomial. The coefficients of the polynomials in numerators are rational numbers, the bounds on their denominators are established with the help of the theorem proved by T. Ohtsuki in Appendix 2. Similarly to the previously considered case of S^3, the U(1)-reducible connection contribution determines the trivial connection contribution into the Witten-Reshetikhin-Turaev invariant of algebraically connected links. We derive a surgery formula for the U(1)-reducible connection contribution, which relates it to the similar contribution into the colored Jones polynomial of a surgery link in S^3.
dc.description59 pages, LaTeX2e; the text has been substantially changed in order to improve the exposition
dc.identifierhttps://arxiv.org/abs/math/9806066
dc.identifierhttp://arxiv.org/abs/math/9806066
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77033
dc.subjectQuantum Algebra
dc.subject57M25
dc.titleA contribution of a U(1)-reducible connection to quantum invariants of links II: Links in rational homology spheres
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