A geometric model of the derived category of skew-gentle algebras

Abstract: Geometric models of certain kinds of categories have been helpful to link several branches of mathematics. For example, the geometric model of the derived categories of the well-known gentle algebras provides a nice like between representation theory of algebras and symplectic topology. In recent work, we provided a geometric model of the objects of the bounded derived category of a skew-gentle algebra (a natural generalisation of gentle algebras) in the form of graded curves in an orbifold dissection with orbifold points of order two with boundary and punctures.

In this talk, we show that this model also provides a nice interpretation of morphisms between complexes. More precisely, we show that intersections of graded curves in orbifolds dissections induce maps between their respective associated complex. We also show that not every map between two complexes arises of this form. This is a work in progress.

Mathematics

Audience: researchers in the topic

Summer Research School: Topological Fukaya categories of surfaces with stops via gentle algebras

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