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Category Theory and its Applications
November 10, 2017 15:30–17:00, Moscow, International laboratory for Mirror Symmetry and Automorphic Forms, 6 Usacheva ul.
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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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Abstract:
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.
Language: English
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