Massey products, A_∞-algebras, differential equations, and Chekanov homology

DOI

10.1080/14029251.2015.1056616How to use a DOI?

Keywords

A∞-algebras; Legendrian contact homology; Kadomtsev-Petviashvili hierarchy

Abstract

We consider (classical and generalized) Massey products on the Chekanov homology of a Legendrian knot, and we prove that they are invariant under Legendrian isotopies. We also construct a minimal A_∞-algebra structure on the Chekanov algebra of a Legendrian knot, we prove that this structure is invariant under Legendrian isotopy, and we observe that its higher multiplications allow us to find representatives for classical Massey products. Finally, we consider differential equations: we remark that the Massey product Legendrian invariants admit a “dynamical interpretation”, in the sense that they provide solutions for a Maurer-Cartan equation posed on an infinite-dimensional bigraded Lie algebra, and we show how to set up and solve a (twisted) Kadomtsev-Petviashvili hierarchy of equations starting from the Chekanov algebra of a Legendrian knot.

Copyright

© 2015 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Lida Mendoza
AU  - Enrique G. Reyes
PY  - 2021
DA  - 2021/01/06
TI  - Massey products, A∞-algebras, differential equations, and Chekanov homology
JO  - Journal of Nonlinear Mathematical Physics
SP  - 342
EP  - 360
VL  - 22
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2015.1056616
DO  - 10.1080/14029251.2015.1056616
ID  - Mendoza2021
ER  -