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Lie bialgebra structure on cyclic cohomology of Fukaya categories

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Abstract

Let M be an exact symplectic manifold with contact type boundary such that c 1(M) = 0. Motivated by noncommutative symplectic geometry and string topology, we show that the cyclic cohomology of the Fukaya category of M has an involutive Lie bialgebra structure.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610064, China

    Xiaojun Chen

  2. School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Hai-Long Her

  3. Department of Mathematics, Capital Normal University, Beijing, 100048, China

    Shanzhong Sun

  4. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing, 100048, China

    Shanzhong Sun

Authors
  1. Xiaojun Chen
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  2. Hai-Long Her
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  3. Shanzhong Sun
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Correspondence to Shanzhong Sun.

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Chen, X., Her, HL. & Sun, S. Lie bialgebra structure on cyclic cohomology of Fukaya categories. Front. Math. China 10, 1057–1085 (2015). https://doi.org/10.1007/s11464-015-0440-8

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  • DOI: https://doi.org/10.1007/s11464-015-0440-8

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