Torsion Invariants of Combed 3-Manifolds with Boundary Pattern and Legendrian Links

Combed 3-Manifolds with Concave Boundary, Framed Links, and Pseudo-Legendrian Links

We provide combinatorial realizations, according to the usual objects/moves scheme, of the following three topological categories: (1) pairs (M,v) where M is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field, up to homotopy; here possibly the boundary of M is non-empty and v may be tangent to the boundary, but only in a concave fashion, and homotopy should preserve tangency type; (2) framed links L in M, up to framed isotopy; (3) triples (M,v,L), with (M,v) as above and L transversal to v, up to pseudo-Legendrian isotopy (transversality-preserving simultaneous homotopy…

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

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 Legendria…

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

We generalize Turaev's definition of torsion invariants of pairs $(M,ξ)$, where $M$ is a 3-dimensional manifold and $ξ$ 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 $ξ$ 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 …

Legendrian 不变量与半 Giroux 扭转

Legendrian invariants and half Giroux torsion

本文研究了具有非零接触不变量的 Legendrian 链环，证明了零调链环在特定过度扭转接触结构中存在非松散实现，并揭示分离半 Giroux 扭转不必然使不变量消失，最后提出关于链环不变量非零性的猜想刻画。

线性化切触同调中 Legendrian 纽结的挠元

Torsion in linearized contact homology for Legendrian knots

本文构造了 $\mathbb{R}^3$ 中 Legendrian 纽结，其线性化切触同调在整数环上含挠元，从而表明存在非精确填充诱导的增广，但其模 2 约化可诱导。

透镜空间中的非宽松 Legendrian Hopf 链环

Non-loose Legendrian Hopf links in lens spaces

本文给出了透镜空间中非宽松 Legendrian Hopf 链环的完整分类，推广了先前结果，并提供了无 Giroux 扭转情形的接触手术图算法。