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 with an extra order 1 generator (Maslov index) added.
@article{bwmeta1.element.bwnjournal-article-bcpv50z1p107bwm,
author = {Goryunov, Victor and Hill, Jonathan},
title = {Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant},
journal = {Banach Center Publications},
volume = {50},
year = {1999},
pages = {107-122},
zbl = {0948.57005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv50z1p107bwm}
}
Goryunov, Victor; Hill, Jonathan. Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant. Banach Center Publications, Tome 50 (1999) pp. 107-122. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv50z1p107bwm/
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