Pushing forward matrix factorizations
Tobias Dyckerhoff,Daniel Murfet +1 more
62
TL;DR: In this paper, the pushforward of a matrix factorization along a ring morphism is described in terms of an idempotent defined using relative Atiyah classes, and the convolution of kernels defining integral functors between categories of matrix factorizations is studied.
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Abstract: We describe the pushforward of a matrix factorization along a ring morphism in terms of an idempotent defined using relative Atiyah classes, and we use this construction to study the convolution of kernels defining integral functors between categories of matrix factorizations. We give an elementary proof of a formula for the Chern character of the convolution generalizing the Hirzebruch–Riemann–Roch formula of Polishchuk and Vaintrob.
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Citations
Coherent analogues of matrix factorizations and relative singularity categories
TL;DR: In this paper, the authors define the triangulated category of relative singularities of a closed subscheme in a scheme, and prove a version of the Thomason-Trobaugh-Neeman localization theorem for coherent matrix factorizations.
Computing Khovanov–Rozansky homology and defect fusion
Nils Carqueville,Daniel Murfet +1 more
TL;DR: The categorified sl(N) link invariants as defined by Khovanov and Rozansky are computed, for various links and values of N, made tractable by an algorithm for reducing tensor products of matrix factorisations to finite rank.
Adjunctions and defects in Landau Ginzburg models
Nils Carqueville,Daniel Murfet +1 more
TL;DR: In this article, the existence of adjoints in this bicategory and formulas for the evaluation and coevaluation maps in terms of Atiyah classes and homological perturbation are presented.
87
Orbifolds and Topological Defects
TL;DR: In this article, it was shown that if the TFT arises as the twist of a superconformal field theory, it is possible to recover results on the Neveu-Schwarz and Ramond sectors of the orbifold theory from a novel, universal perspective.
63
Deformations of colored sl(N) link homologies via foams
David E. V. Rose,Paul Wedrich +1 more
TL;DR: In this paper, the authors generalize results of Lee, Gornik and Wu on the structure of deformed colored sl(N) link homologies to the case of non-generic deformations.
57
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