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Three-dimensional topological field theory and symplectic algebraic geometry II

Kapustin, Anton and Rozansky, Lev (2010) Three-dimensional topological field theory and symplectic algebraic geometry II. Communications in Number Theory and Physics, 4 (3). pp. 463-549. ISSN 1931-4523. doi:10.4310/CNTP.2010.v4.n3.a1.

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Motivated by the path-integral analysis [6] of boundary conditions in a three-dimensional topological sigma model, we suggest a definition of the two-category ¨L(X) associated with a holomorphic symplectic manifold X and study its properties. The simplest objects of ¨L(X) are holomorphic lagrangian submanifolds Y ⊂ X. We pay special attention to the case when X is the total space of the cotangent bundle of a complex manifold U or a deformation thereof. In the latter case, the endomorphism category of the zero section is a monoidal category which is an A_∞ deformation of the two-periodic derived category of U.

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URLURL TypeDescription Paper
Kapustin, Anton0000-0003-3903-5158
Additional Information:© 2010 International Press. Received March 11, 2010. L.R. is indebted to D. Arinkin for many patient explanations of the properties of coherent sheaves. He is also grateful to V. Ginzburg for numerous discussions and encouragement. A.K. would like to thank D. Orlov for the same. A.K. is also grateful to D. Ben-Zvi, V. Ostrik, and L. Positselski for advice. Both authors would like to thank Natalia Saulina for collaboration on Part I of the paper. The work of A.K. was supported in part by the DOE grant DE-FG03-92-ER40701. The work of L.R. was supported by the NSF grant DMS-0808974.
Group:Caltech Theory
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG03-92-ER40701
Issue or Number:3
Record Number:CaltechAUTHORS:20110314-113130491
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:22858
Deposited On:15 Mar 2011 14:48
Last Modified:09 Nov 2021 16:08

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