Mathematics – Geometric Topology
Scientific paper
1999-07-29
Manuscripta Math. 106 (2001), 13-74
Mathematics
Geometric Topology
49 pages, 31 figures
Scientific paper
We generalize Turaev's definition of torsion invariants of pairs $(M,\xi)$, where $M$ is a 3-dimensional manifold and $\xi$ is an Euler structure on $M$ (a non-singular vector field up to homotopy relative to the boundary of $M$ and local modifications in the interior of $M$). Namely, we allow $M$ to have arbitrary boundary and $\xi$ to have simple (convex and/or concave) tangency circles to the boundary. We prove that Turaev's $H_1(M)$-equivariance formula holds also in our generalized context. Our torsions apply in particular to (the exterior of) Legendrian links (in particular, knots) in contact 3-manifolds, and we prove that they can distinguish knots which are isotopic as framed knots but not as Legendrian knots. Using the combinatorial encoding of vector fields based on branched standard spines we show how to explicitly invert Turaev's reconstruction map from combinatorial to smooth Euler structures, thus making the computation of torsions a more effective one. As an example we work out a specific computation.
Benedetti Riccardo
Petronio Carlo
No associations
LandOfFree
Reidemeister Torsion of 3-Dimensional Euler Structures with Simple Boundary Tangency and Legendrian Knots 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 Reidemeister Torsion of 3-Dimensional Euler Structures with Simple Boundary Tangency and Legendrian Knots, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reidemeister Torsion of 3-Dimensional Euler Structures with Simple Boundary Tangency and Legendrian Knots will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-420864