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Теория категорий и её приложения
10 ноября 2017 г. 15:30–17:00, г. Москва, Международная лаборатория зеркальной симметрии и автоморфных форм, ВШЭ, ул. Усачева, д. 6, ауд. 215
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Functions on moduli spaces from cyclic homology
Ch. Brav National Research University "Higher School of Economics" (HSE), Moscow
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Эта страница: | 164 |
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Аннотация:
We discuss the 'moduli of objects' M_D in a dg category
D and construct a map from cyclic homology of D to functions on
the moduli space M_D. When D is a smooth, oriented dg
category ('Calabi-Yau'), the cyclic homology HC(D) is
endowed with a shifted Lie bracket ('algebraic
string bracket') and the functions on M_D are
endowed with a shifted Poisson bracket. We show
that the map from cyclic homology to functions entwines
the brackets. Examples include the Goldmann bracket of
free loops on a surface, the string bracket of
Chas-Sullivan, and the Hitchen system for Higgs
bundles. This is joint work very much in progress with
Nick Rozenblyum.
Язык доклада: английский
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