Reidemeister Torsion of 3-Dimensional Euler Structures with Simple Boundary Tangency and Pseudo-Legendrian Knots

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dc.creatorBenedetti, Riccardo
dc.creatorPetronio, Carlo
dc.date2000-02-17
dc.date.accessioned2026-07-07T04:33:56Z
dc.date.available2026-07-07T04:33:56Z
dc.descriptionWe 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.
dc.descriptionThis is a revised version of math.GT/9907184, submitted as a new paper because the understanding of torsion of pseudo-Legendrian knots is here substantially improved
dc.identifierhttps://arxiv.org/abs/math/0002143
dc.identifierhttp://arxiv.org/abs/math/0002143
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58714
dc.subjectGeometric Topology
dc.subject57M27
dc.titleReidemeister Torsion of 3-Dimensional Euler Structures with Simple Boundary Tangency and Pseudo-Legendrian Knots
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