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117
DG quotients of DG categories
 J. ALGEBRA
, 2008
"... 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 152 (0 self)
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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 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 59 (8 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
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 56 (5 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, 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 53 (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.
Compact generators in categories of matrix factorizations
 MR2824483 (2012h:18014), Zbl 1252.18026, arXiv:0904.4713
"... Abstract. We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. We exhibit the stabilized residue field as a compact generator. This implies a quasiequivalence between the category of matrix factorizations and the dg derived category of an ex ..."
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Cited by 52 (1 self)
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Abstract. We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. We exhibit the stabilized residue field as a compact generator. This implies a quasiequivalence between the category of matrix factorizations and the dg derived category of an explicitly computable dg algebra. Building on this quasiequivalence we establish a derived Morita theory which identifies the functors between matrix factorization categories as integral transforms. This enables us to calculate the Hochschild chain and cochain complexes of matrix factorization categories. Finally, we give interpretations of the results of this work in terms of noncommutative geometry modelled on dg categories. Contents
Homological mirror symmetry for the genus two curve
"... The Homological Mirror Symmetry conjecture relates symplectic and algebraic geometry through their associated categorical structures. Kontsevich’s original version [31] concerned ..."
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Cited by 48 (2 self)
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The Homological Mirror Symmetry conjecture relates symplectic and algebraic geometry through their associated categorical structures. Kontsevich’s original version [31] concerned
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 47 (2 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.