Categorification of Seidel's representation

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• 作者：François Charette ; Octav Cornea
• 刊名：Israel Journal of Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：211
• 期：1
• 页码：67-104
• 全文大小：480 KB
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• 作者单位：François Charette (1)
  Octav Cornea (2)
  
  1. Max Planck Institute for Mathematics, Vivatsgasse 7, 53111, Bonn, Germany
  2. Department of Mathematics and Statistics University of Montreal, C.P. 6128 Succ. Centre-Ville, Montreal, QC, H3C 3J7, Canada
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Algebra
  Group Theory and Generalizations
  Analysis
  Applications of Mathematics
  Mathematical and Computational Physics
  
• 出版者：Hebrew University Magnes Press
• ISSN：1565-8511

文摘

Two natural symplectic constructions, the Lagrangian suspension and Seidel’s quantum representation of the fundamental group of the group of Hamiltonian diffeomorphisms, Ham(M), with (M, ω) a monotone symplectic manifold, admit categorifications as actions of the fundamental groupoid Π(Ham(M)) on a cobordism category recently introduced in [BC14] and, respectively, on a monotone variant of the derived Fukaya category. We show that the functor constructed in [BC14] that maps the cobordism category to the derived Fukaya category is equivariant with respect to these actions.