Low-dimensional Topology and Algebraic Geometry Seminar: P. Popov

Dear students,

Please join us at the next meeting of the Low-dimensional Topology and
Algebraic Geometry seminar.

https://math.hse.ru/lowdimtop/

As usual, there will be plenty of snacks!

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Math Department of the Higher School of Economics, Room 326
Thursday March 15, 10:30-12:00

Speaker: Pavel Popov

Title: Character varieties and Heegaard splittings

Abstract:
 Let T be a topological space. By a character variety X(T) of T we
will understand some moduli space of representations of pi_1(T) in
SL(2,C). In the case of a 3-manifold M with a Heegaard decomposition
into U_1 and U_2 along a surface S, it turns out that the smooth locus
of X(S) has a symplectic structure and X(U_1), X(U_2) are Lagrangian
subvarieties. In the paper arXiv:1708.00289v1, the authors constructed
invariants of M using the "derived Lagrangian intersection" of X(U_1)
and X(U_2). This is our motivation. In this elementary talk we will
introduce the notion of character varieties, study their tangent
spaces, and consider some examples. After that we will describe a
symplectic structure on X(S) and show that X(U_1) and X(U_2) are
Lagrangian.