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Product structures for Legendrian contact homology

Civan, Gokhan and Koprowski, Paul and Etnyre, John and Sabloff, Joshua M. and Walker, Alden (2011) Product structures for Legendrian contact homology. Mathematical Proceedings of the Cambridge Philosophical Society, 150 (2). pp. 291-311. ISSN 0305-0041.

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Legendrian contact homology (LCH) is a powerful non-classical invariant of Legendrian knots. Linearization makes the LCH computationally tractable at the expense of discarding nonlinear (and non-commutative) information. To recover some of the nonlinear information while preserving computability, we introduce invariant cup and Massey products – and, more generally, an A∞ structure – on the linearized LCH. We apply the products and A∞ structure in three ways: to find infinite families of Legendrian knots that are not isotopic to their Legendrian mirrors, to reinterpret the duality theorem of the fourth author in terms of the cup product, and to recover higher-order linearizations of the LCH.

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Additional Information:© 2010 Cambridge Philosophical Society. Received 10 February 2010; revised 27 May 2010. First published online 2 December 2010. The authors thank Jim Stasheff for several helpful discussions. The first author was supported by an REU through NSF grant DMS-0739343. The third author was partially supported by NSF grant DMS-0804820. The second and fifth authors were supported as undergraduate summer research students by the Haverford College faculty support fund. The fourth author was partially supported by NSF grant DMS-0909273.
Funding AgencyGrant Number
NSF Research Experiences for Undergraduates (REU)DMS-0739343
Haverford College faculty support fundUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20110314-131739542
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22861
Deposited By: Tony Diaz
Deposited On:15 Mar 2011 21:41
Last Modified:03 Oct 2019 02:41

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