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News

05.11.2019

“Goldman brackets, Turaev cobrackets, and moduli of flat connections”

Anton Alexeev (University of Geneva)

Colloquium of Department of Mathematics and Computer Science

Thursday 7 November 17:15 room 105 (14-th line V.I., 29)

Abstract

 

Moduli of flat connections on oriented two-dimensional manifolds are considered to be one of the most interesting and popular examples of the sympletic spaces. Sympletic structure has been identified by Atiyah and Bott, and its combinatoric description has been giben by Goldman. The Goldman bracket is defined on homotopy loop classes in terms of intersections of curves.

Turaev proposed a cobracket construction that uses self-intersecting curves. The Goldman bracket and the Turaev cobracket are consistent with each other and determine the structure of the Lie bialgebra. A new interpretation of the Turaev co-bracket in terms of modules of plane connections will be presented during the lecture. This interpretation is based on the Batalin-Vilkovisky structure, generalizing the symplectic structure.

All the aforementioned terms will be defined in the report. The report is based on the cooperation with F. Nef, Y.Pullman and P. Shevera.

Everyone is welcome!