RESEARCH ARTICLE

Lie bialgebra structure on cyclic cohomology of Fukaya categories

  • Xiaojun CHEN 1 ,
  • Hai-Long HER 2 ,
  • Shanzhong SUN , 3,4
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  • 1. Department of Mathematics, Sichuan University, Chengdu 610064, China
  • 2. School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
  • 3. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048,
  • 4. Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, China

Received date: 14 Apr 2014

Accepted date: 24 Oct 2014

Published date: 24 Jun 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let M be an exact symplectic manifold with contact type boundary such that c1(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.

Cite this article

Xiaojun CHEN , Hai-Long HER , Shanzhong SUN . Lie bialgebra structure on cyclic cohomology of Fukaya categories[J]. Frontiers of Mathematics in China, 2015 , 10(5) : 1057 -1085 . DOI: 10.1007/s11464-015-0440-8

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