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.
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.
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[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.
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[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.