Colored alexander invariants and cone-manifolds

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Abstract

In this paper, we reconstruct the link invariant of framed links introduced in [1] by the universal R-matrix of Uq(sl2) and name it the colored Alexander invariant. We check that the optimistic limit o-lim of this invariant is determined by the volume of the knot and link cone-manifold for figure eight knot, Whitehead link and Borromean rings. We also propose the A-polynomials of these examples obtained from the colored Alexander invariant.

Original languageEnglish
Pages (from-to)541-564
Number of pages24
JournalOsaka Journal of Mathematics
Volume45
Issue number2
Publication statusPublished - 2008 Jun 1

ASJC Scopus subject areas

  • Mathematics(all)

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