Mathematics – Geometric Topology
Scientific paper
2008-01-10
Mathematics
Geometric Topology
40 pages, 23 figures
Scientific paper
We 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.
Pervova Ekaterina
Petronio Carlo
No associations
LandOfFree
On colored Turaev-Viro invariants for links in arbitrary 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On colored Turaev-Viro invariants for links in arbitrary 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On colored Turaev-Viro invariants for links in arbitrary 3-manifolds will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-436556