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## Banach Center Publications

1999 | 50 | 1 | 107-122
Tytuł artykułu

### Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant

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Języki publikacji
EN
Abstrakty
EN
We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in $R^3$ with an extra order 1 generator (Maslov index) added.
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Tom
Numer
Strony
107-122
Opis fizyczny
Daty
wydano
1999
Twórcy
autor
• Department of Mathematical Sciences, Division of Pure Mathematics, The University of Liverpool, Liverpool L69 3BX, U.K.
autor
• Department of Mathematical Sciences, Division of Pure Mathematics, The University of Liverpool, Liverpool L69 3BX, U.K.
Bibliografia
• [1] V. I. Arnol'd, Plane curves, their invariants, perestroikas and classifications, in: Singularities and Bifurcations, V. I. Arnold (ed.), Adv. Soviet Math. 21, Amer. Math. Soc., Providence, 1994, 33-91.
• [2] V. I. Arnol'd, Topological Invariants of Plane Curves and Caustics, University Lecture Series 5, Amer. Math. Soc., Providence, 1994.
• [3] V. I. Arnol'd, Invariants and perestroikas of plane fronts (in Russian), Trudy Mat. Inst. Steklov. 209 (1995), 14-64; English transl.: Proc. Steklov Inst. Mat. 209 (1995), 11-56.
• [4] D. Bar-Natan, On the Vassiliev knot invariants, Topology 34 (1995), 423-472.
• [5] V. V. Goryunov, Vassiliev type invariants in Arnold's $J^+$-theory of plane curves without direct self-tangencies, Topology 37 (1998), 603-620.
• [6] V. V. Goryunov, Vassiliev invariants of knots in $R^3$ and in a solid torus, in: Differential and Symplectic Topology of Knots and Curves, S. Tabachnikov (ed.), Amer. Math. Soc. Transl. Ser. 2, 190, Amer. Math. Soc., Providence, 1999, 37-59.
• [7] V. V. Goryunov, Finite order invariants of framed knots in a solid torus and in Arnold's $J^+$-theory of plane curves, in: Geometry and Physics, J. E. Andersen, J. Dupont, H. Pedersen and A. Swann (eds.), Lecture Notes in Pure and Appl. Math. 184, Marcel Dekker, New York, 1997, 549-556.
• [8] J. W. Hill, Vassiliev-type invariants of planar fronts without dangerous self-tangencies, C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), 537-542.
• [9] M. Kontsevich, Vassiliev's knot invariants, in: I. M. Gel'fand Seminar, S. Gel'fand, S. Gindikin (eds.), Adv. Soviet Math. 16, Part 2, Amer. Math. Soc., Providence, 1993, 137-150.
• [10] V. A. Vassiliev, Cohomology of knot spaces, in: Theory of Singularities and its Applications, V. I. Arnol'd (ed.), Adv. Soviet Math. 1, Amer. Math. Soc., Providence, 1990, 23-69.
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