Title
On deformations of triangulated models On deformations of triangulated models
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
New York, N.Y. ,
Subject
Mathematics
Source (journal)
Advances in mathematics. - New York, N.Y.
Volume/pages
243(2013) , p. 330-374
ISSN
0001-8708
ISI
000320632900012
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
This paper is the first part of a project aimed at understanding deformations of triangulated categories, and more precisely their dg and A∞A∞ models, and applying the resulting theory to the models occurring in the Homological Mirror Symmetry setup. In this first paper, we focus on models of derived and related categories, based upon the classical construction of twisted objects over a dg or A∞A∞-algebra. For a Hochschild 2 cocycle on such a model, we describe a corresponding curvature compensating deformation which can be entirely understood within the framework of twisted objects. We unravel the construction in the specific cases of derived A∞A∞ and abelian categories, homotopy categories, and categories of graded free qdg-modules. We identify a purity condition on our models which ensures that the structure of the model is preserved under deformation. This condition is typically fulfilled for homotopy categories, but not for unbounded derived categories.
E-info
https://repository.uantwerpen.be/docman/iruaauth/4352f7/af0894dc591.pdf
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