On colored Turaev-Viro invariants for links in arbitrary 3-manifolds

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dc.creatorPervova, Ekaterina
dc.creatorPetronio, Carlo
dc.date2008-01-10
dc.date.accessioned2026-07-07T08:53:41Z
dc.date.available2026-07-07T08:53:41Z
dc.descriptionWe consider certain invariants of links in 3-manifolds, obtained by a specialization of the Turaev-Viro invariants of 3-manifolds, that we call colored Turaev-Viro invariants. Their construction is based on a presentation of a pair (M,L), where M is a closed oriented 3-manifold and L is an oriented link in M, by a triangulation of M such that each component of L is an edge. We analyze some basic properties of these invariants, including the behavior under connected sums of pairs away and along links. These properties allow us to provide examples of links in the three-sphere having the same HOMFLY polynomial and the same Kauffman polynomial but distinct Turaev-Viro invariants, and similar examples for the Alexander polynomial. We also investigate the relations between the Turaev-Viro invariants of (M,L) and those of the complement of L in M, showing that they are sometimes but not always determined by each other.
dc.description40 pages, 23 figures
dc.identifierhttps://arxiv.org/abs/0801.1620
dc.identifierhttp://arxiv.org/abs/0801.1620
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145706
dc.subjectGeometric Topology
dc.subject57M27
dc.titleOn colored Turaev-Viro invariants for links in arbitrary 3-manifolds
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