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Categories of curved complexes for marked surfaces

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HTL - Homology theories in low dimensional topology

In 2014, Haiden, Katzarkov and Kontsevich gave a complete algebraic description of the Fukaya category of immersed curves on oriented surfaces with boundary. In this talk, I will introduce dg categories which I suspect to be closely related, if not equivalent, to those Fukaya categories. The objects of these dg categories are curved complexes, which, loosely speaking, are chain complexes whose differentials square to multiples of the identity. As an application, I will mainly focus on two examples of such categories arising from Heegaard Floer theory and discuss why they might be interesting.



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