Autor:	Vladimir Tchernov
Rok vydání:	2003
Předmět:	Algebra Pure mathematics Algebra and Number Theory Mathematics::Quantum Algebra Structure (category theory) Tangent Vector field Isomorphism Mathematics::Algebraic Topology Mathematics::Symplectic Geometry Mathematics::Geometric Topology Mathematics
Zdroj:	Compositio Mathematica. 135:103-122
ISSN:	0010-437X
DOI:	10.1023/a:1021733206049
Popis:	The study of the Vassiliev invariants of Legendrian knots was started by D. Fuchs and S. Tabachnikov who showed that the groups of C-valued Vassiliev invariants of Legendrian and of framed knots in the standard contact R3 are canonically isomorphic. Recently we constructed the first examples of contact 3-manifolds where Vassiliev invariants of Legendrian and of framed knots are different. Moreover in these examples Vassiliev invariants of Legendrian knots distinguish Legendrian knots that are isotopic as framed knots and homotopic as Legendrian immersions. This raised the question what information about Legendrian knots can be captured using Vassiliev invariants. Here we answer this question by showing that for any contact 3-manifold with a cooriented contact structure the groups of Vassiliev invariants of Legendrian knots and of knots that are nowhere tangent to a vector field that coorients the contact structure are canonically isomorphic.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4f28f68539b73a336e83887fa4f98f88 https://doi.org/10.1023/a:1021733206049 Zobrazit plný text záznamu Full text from SpringerLink