Results 1  10
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63
DG quotients of DG categories
 J. Algebra
"... Abstract. Keller introduced a notion of quotient of a differential graded category modulo a full differential graded subcategory which agrees with Verdier’s notion of quotient of a triangulated category modulo a triangulated subcategory. This work is an attempt to further develop his theory. ..."
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Cited by 79 (0 self)
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Abstract. Keller introduced a notion of quotient of a differential graded category modulo a full differential graded subcategory which agrees with Verdier’s notion of quotient of a triangulated category modulo a triangulated subcategory. This work is an attempt to further develop his theory.
Dbranes, Categories and N = 1 Supersymmetry
, 2000
"... We show that boundary conditions in topological open string theory on CalabiYau manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with conformal field theory considerations, this leads to a precise crit ..."
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Cited by 42 (0 self)
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We show that boundary conditions in topological open string theory on CalabiYau manifolds are objects in the derived category of coherent sheaves, as foreseen in the homological mirror symmetry proposal of Kontsevich. Together with conformal field theory considerations, this leads to a precise criterion determining the BPS branes at any point in CY moduli space, completing the proposal of Πstability.
Computation Of Superpotentials For Dbranes
, 2004
"... We present a general method for the computation of treelevel superpotentials for the worldvolume theory of Btype Dbranes. This includes quiver gauge theories in the case that the Dbrane is marginally stable. The technique involves analyzing the A∞structure inherent in the derived category of co ..."
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Cited by 38 (2 self)
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We present a general method for the computation of treelevel superpotentials for the worldvolume theory of Btype Dbranes. This includes quiver gauge theories in the case that the Dbrane is marginally stable. The technique involves analyzing the A∞structure inherent in the derived category of coherent sheaves. This effectively gives a practical method of computing correlation functions in holomorphic Chern–Simons theory. As an example, we give a more rigorous proof of previous results concerning
Dbranes on CalabiYau manifolds
, 2004
"... In this review we study BPS Dbranes on Calabi–Yau threefolds. Such Dbranes naturally divide into two sets called Abranes and Bbranes which are most easily understood from topological field theory. The main aim of this paper is to provide a selfcontained guide to the derived category approach to ..."
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Cited by 35 (7 self)
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In this review we study BPS Dbranes on Calabi–Yau threefolds. Such Dbranes naturally divide into two sets called Abranes and Bbranes which are most easily understood from topological field theory. The main aim of this paper is to provide a selfcontained guide to the derived category approach to Bbranes and the idea of Πstability. We argue that this mathematical machinery is hard to avoid for a proper understanding of Bbranes. Abranes and Bbranes are related in a very complicated and interesting way which ties in with the “homological mirror symmetry ” conjecture of Kontsevich. We motivate and exploit this form of mirror symmetry. The examples of the quintic 3fold, flops and orbifolds are discussed at some length. In the latter
The Diagonal of the Stasheff polytope
"... We construct an Ainfinity structure on the tensor product of two Ainfinity algebras by using the simplicial decomposition of the Stasheff polytope. The key point is the construction of an operad AAinfinity based on the simplicial Stasheff polytope. The operad AAinfinity admits a coassociative ..."
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Cited by 33 (1 self)
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We construct an Ainfinity structure on the tensor product of two Ainfinity algebras by using the simplicial decomposition of the Stasheff polytope. The key point is the construction of an operad AAinfinity based on the simplicial Stasheff polytope. The operad AAinfinity admits a coassociative diagonal and the operad Ainfinity is a retract by deformation of it. We compare these constructions with analogous constructions due to SaneblidzeUmble and MarklShnider based on the BoardmanVogt cubical decomposition of the Stasheff polytope.
Dbrane dynamics and Dbrane categories
 JHEP
"... This is a short nontechnical note summarizing the motivation and results of my recent work on Dbrane categories. I also give a brief outline of how this framework can be applied to study the dynamics of topological Dbranes and why this has a bearing on the homological mirror symmetry conjecture. T ..."
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Cited by 25 (11 self)
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This is a short nontechnical note summarizing the motivation and results of my recent work on Dbrane categories. I also give a brief outline of how this framework can be applied to study the dynamics of topological Dbranes and why this has a bearing on the homological mirror symmetry conjecture. This note can be read without any
Obstructed Dbranes in LandauGinzburg orbifolds
 Adv. Theor. Math. Phys
"... We study deformations of LandauGinzburg Dbranes corresponding to obstructed rational curves on CalabiYau threefolds. We determine Dbrane moduli spaces and Dbrane superpotentials by evaluating higher products up to homotopy in the LandauGinzburg orbifold category. For concreteness we work out t ..."
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Cited by 20 (2 self)
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We study deformations of LandauGinzburg Dbranes corresponding to obstructed rational curves on CalabiYau threefolds. We determine Dbrane moduli spaces and Dbrane superpotentials by evaluating higher products up to homotopy in the LandauGinzburg orbifold category. For concreteness we work out the details for lines on a perturbed Fermat quintic. In this case we show that our results reproduce the local analytic structure of the Hilbert scheme of curves on the threefold.
Exact Lagrangian submanifolds in simplyconnected cotangent bundles,” math.SG/0701783
"... Abstract. We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second StiefelWhitney class of the Lagrangian submanifold) we prove such submanifolds are Floerc ..."
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Abstract. We consider exact Lagrangian submanifolds in cotangent bundles. Under certain additional restrictions (triviality of the fundamental group of the cotangent bundle, and of the Maslov class and second StiefelWhitney class of the Lagrangian submanifold) we prove such submanifolds are Floercohomologically indistinguishable from the zerosection. This implies strong restrictions on their topology. An essentially equivalent result was recently proved independently by Nadler [16], using a different approach. 1.