A microlocal category associated to a symplectic manifold

Boris L Tsygan*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

For a symplectic manifold subject to certain topological conditions a category enriched in ∞ local systems of modules over the Novikov ring is constructed. The construction is based on the category of modules over Fedosov’s deformation quantization algebra that have an additional structure, namely an action of the fundamental groupoid up to inner automorphisms. Based in large part on the ideas of Bressler-Soibelman, Feigin, and Karabegov, it motivated by the theory of Lagrangian distributions and is related to other microlocal constructions of a category starting from a symplectic manifold, such as those due to Nadler-Zaslow and Tamarkin. In the case when our manifold is a flat two-torus, the answer is very close to both the Tamarkin microlocal category and the Fukaya category as computed by Polishchuk and Zaslow.

Original languageEnglish (US)
Title of host publicationAlgebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013
EditorsMichael Hitrik, Dmitry Tamarkin, Boris Tsygan, Steve Zelditch
PublisherSpringer New York LLC
Pages225-337
Number of pages113
ISBN (Print)9783030015862
DOIs
StatePublished - Jan 1 2018
EventWorkshop on Algebraic and Analytic Microlocal Analysis, AAMA 2013 - Evanston, United States
Duration: May 20 2013May 24 2013

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume269
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherWorkshop on Algebraic and Analytic Microlocal Analysis, AAMA 2013
CountryUnited States
CityEvanston
Period5/20/135/24/13

Fingerprint

Symplectic Manifold
Enriched Category
Deformation Quantization
Module
Local System
Groupoid
Automorphisms
Torus
Ring
Algebra

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Tsygan, B. L. (2018). A microlocal category associated to a symplectic manifold. In M. Hitrik, D. Tamarkin, B. Tsygan, & S. Zelditch (Eds.), Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013 (pp. 225-337). (Springer Proceedings in Mathematics and Statistics; Vol. 269). Springer New York LLC. https://doi.org/10.1007/978-3-030-01588-6_4
Tsygan, Boris L. / A microlocal category associated to a symplectic manifold. Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013. editor / Michael Hitrik ; Dmitry Tamarkin ; Boris Tsygan ; Steve Zelditch. Springer New York LLC, 2018. pp. 225-337 (Springer Proceedings in Mathematics and Statistics).
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Tsygan, BL 2018, A microlocal category associated to a symplectic manifold. in M Hitrik, D Tamarkin, B Tsygan & S Zelditch (eds), Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013. Springer Proceedings in Mathematics and Statistics, vol. 269, Springer New York LLC, pp. 225-337, Workshop on Algebraic and Analytic Microlocal Analysis, AAMA 2013, Evanston, United States, 5/20/13. https://doi.org/10.1007/978-3-030-01588-6_4

A microlocal category associated to a symplectic manifold. / Tsygan, Boris L.

Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013. ed. / Michael Hitrik; Dmitry Tamarkin; Boris Tsygan; Steve Zelditch. Springer New York LLC, 2018. p. 225-337 (Springer Proceedings in Mathematics and Statistics; Vol. 269).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Tsygan BL. A microlocal category associated to a symplectic manifold. In Hitrik M, Tamarkin D, Tsygan B, Zelditch S, editors, Algebraic and Analytic Microlocal Analysis - AAMA, Evanston, Illinois, USA, 2012 and 2013. Springer New York LLC. 2018. p. 225-337. (Springer Proceedings in Mathematics and Statistics). https://doi.org/10.1007/978-3-030-01588-6_4