Mathematics – Geometric Topology
Scientific paper
2000-02-17
Mathematics
Geometric Topology
This is a revised version of math.GT/9907184, submitted as a new paper because the understanding of torsion of pseudo-Legendri
Scientific paper
We generalize Turaev's definition of torsion invariants of pairs (M,x), where M is a 3-dimensional manifold and x is an Euler structure on M (a non-singular vector field up to homotopy relative to bM and local modifications in int(M). Namely, we allow M to have arbitrary boundary and x 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) pseudo-Legendrian knots (i.e. knots transversal to a given vector field), and hence to Legendrian knots in contact 3-manifolds. We show that torsion, as an absolute invariant, contains a lifting to pseudo-Legendrian knots of the classical Alexander invariant. We also precisely analyze the information carried by torsion as a relative invariant of pseudo-Legendrian knots which are framed-isotopic. Using branched standard spines to describe vector fields 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 calculation.
Benedetti Riccardo
Petronio Carlo
No associations
LandOfFree
Reidemeister Torsion of 3-Dimensional Euler Structures with Simple Boundary Tangency and Pseudo-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 Pseudo-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 Pseudo-Legendrian Knots will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-312814