New 3CY categories of topological surfaces

Abstract: To a topological surface, perhaps with certain markings, one can attach several different triangulated categories whose objects are, roughly speaking, curves on the surface. One such example is the Fukaya category of the surface, another is the 3-d Calabi-Yau (3CY) category of an ideal triangulation. These have proven useful, among other things, in the study of Bridgeland stability conditions and the representation theory of finite-dimensional algebras. In the recent preprint arXiv:2104.06018 I introduce yet another class of triangulated A-infinity categories of surfaces. The motivation for constructing them was to extend the work of Bridgeland-Smith on stability conditions and quadratic differentials to the finite area case (e.g. holomorphic differentials). They are closely related to the existing triangulated categories of surfaces and clarify the relation between them. Their construction involves some algebraic tricks, such as twisted complexes and modules over curved A-infinity categories, which will be discussed in detail.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: https://us02web.zoom.us/j/87160036709?pwd=aGtBdkx4VDFuY0l2UlkzRFdiYUF3dz09 Meeting ID: 871 6003 6709 Passcode: LAGOON

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