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PAUL KIRK (Indiana/MPI): Lagrangian-Floer homology of traceless SU(2) character varieties of tangle decompositions.



The traceless SU(2) character of a punctured 2-sphere is a singular real algebraic variety with symplectic strata. The traceless SU(2) character variety of a 3-manifold with boundary with a tangle removed (generically) Lagrangian immerses in this symplectic variety. To a tangle decomposition of a link in a 3-manifold one can, in favorable circumstances, assign the Lagrangian-Floer complex of the corresponding pair of immersed lagrangians. I'll discuss joint work (in progress) with Hedden and Herald on carrying out this construction, its relation to the Morse theory of the Chern-Simons function (singular instanton homology), calculations, genericity theorems, and if time permits, using the A_infty structure on the corresponding Fukaya category to construct exact sequences, in the case of the 4-punctured 2-sphere.

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