Kapustin, Anton and Rozansky, Lev (2010) Threedimensional topological field theory and symplectic algebraic geometry II. Communications in Number Theory and Physics, 4 (3). pp. 463549. ISSN 19314523. http://resolver.caltech.edu/CaltechAUTHORS:20110314113130491

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Abstract
Motivated by the pathintegral analysis [6] of boundary conditions in a threedimensional topological sigma model, we suggest a definition of the twocategory ¨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 twoperiodic derived category of U.
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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. BenZvi, 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 DEFG0392ER40701. The work of L.R. was supported by the NSF grant DMS0808974.  
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Record Number:  CaltechAUTHORS:20110314113130491  
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:20110314113130491  
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ID Code:  22858  
Collection:  CaltechAUTHORS  
Deposited By:  Jason Perez  
Deposited On:  15 Mar 2011 14:48  
Last Modified:  27 Oct 2017 18:38 
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