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Руководство
Научный руководитель Ландо Сергей Константинович
Заместитель декана по административной работе Балаева Светлана Васильевна
Заместитель декана по по научной работе Горбунов Василий Геннадьевич
Заместитель декана по учебной работе Колесников Александр Викторович
Заместитель декана по работе с абитуриентами Пятов Павел Николаевич

Low-dim topology and algebraic geometry: P. Popov

Мероприятие завершено

Dear students,

Please join us at the next meeting of the Low-dimensional Topology andAlgebraic 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 22, 10:30-12:00

Speaker: Pavel Popov

Title: Character varieties and Heegaard splittings (Part 2)

Abstract:

In the last talk we introduced a character variety X(Gamma) for agroup Gamma. It is a variety of representations of this group intoSL(2,C). We calculated the tangent spaces to regular irreduciblerepresentations.  If T is a topological space, we denote X(pi_1(T))just as X(T). In this talk we consider the case of a 3-manifold M witha Heegaard decomposition into U_1 and U_2 along a surface S. It turnsout that the smooth locus of X(S) has a symplectic structure andX(U_1), X(U_2) are Lagrangian subvarieties. Using intersection theoryfor X(U_1), X(U_2) we introduce an invariant [Curtis01] lambda(M) of3-manifolds M which, roughly speaking, counts isolated irreduciblerepresentations of pi_1(M). In the end we discuss some results aboutthis invariant and compare it with the more sophisticated invariant of[AM17] which is constructed using the "derived lagrangianintersection" of X(U_1) and X(U_2).

[Curtis01] Cynthia L.Curtis, An intersection theory count of theSL2(C)-representations of the fundamental group of a 3-manifold.

[AM17] Mohammed Abouzaid, Ciprian Manolescu, A sheaf-theoretic modelfor SL(2,C) Floer homology.