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• W2074089660 abstract "We consider S^1-families of Legendrian knots in the standard contact R^3. We define the monodromy of such a loop, which is an automorphism of the Chekanov-Eliashberg contact homology of the starting (and ending) point. We prove this monodromy is a homotopy invariant of the loop. We also establish techniques to address the issue of Reidemeister moves of Lagrangian projections of Legendrian links. As an application, we exhibit a loop of right-handed Legendrian torus knots which is non-contractible in the space Leg(S^1,R^3) of Legendrian knots, although it is contractible in the space Emb(S^1,R^3) of smooth knots. For this result, we also compute the contact homology of what we call the Legendrian closure of a positive braid and construct an augmentation for each such link diagram." @default.
• W2074089660 created "2016-06-24" @default.
• W2074089660 creator A5000253602 @default.
• W2074089660 date "2005-10-26" @default.
• W2074089660 modified "2023-10-06" @default.
• W2074089660 title "Contact homology and one parameter families of Legendrian knots" @default.
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• W2074089660 doi "https://doi.org/10.2140/gt.2005.9.2013" @default.
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