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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Non-commutative Hodge structures: Towards matching categorical and geometric examples


Author: D. Shklyarov
Journal: Trans. Amer. Math. Soc. 366 (2014), 2923-2974
MSC (2010): Primary 16E45, 16E40
Published electronically: January 17, 2014
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Abstract: The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the periodic cyclic homology viewed as a bundle over the punctured formal disk. Our main result says that for the category of matrix factorizations of a polynomial the formulas reproduce, up to a certain shift, a well-known connection on the associated twisted de Rham cohomology which plays a central role in the geometric approach to the Hodge theory of isolated singularities.


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Additional Information

D. Shklyarov
Affiliation: Lehrstuhl für Analysis und Geometrie, Universität Augsburg, Institut für Mathematik, 86135 Augsburg, Germany
Address at time of publication: Freiburg Institute for Advanced Studies, Albert-Ludwigs-Universität Freiburg, Albertstrasse 19, 79104 Freiburg i. Br., Germany
Email: dmytro.shklyarov@math.uni-augsburg.de, dmytro.shklyarov@math.uni-freiburg.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05913-8
PII: S 0002-9947(2014)05913-8
Received by editor(s): September 14, 2011
Received by editor(s) in revised form: June 21, 2012
Published electronically: January 17, 2014
Additional Notes: This research was supported by the ERC Starting Independent Researcher Grant StG No. 204757-TQFT (K. Wendland PI)
Article copyright: © Copyright 2014 American Mathematical Society