Manifold diagrams: Poincaré duality, singularities, and smooth structures

Abstract: We will pick things up just where we left off last week in Manuel's talk. We will discuss combinatorial and geometric models for manifold diagrams (i.e. higher dimensional generalizations of string diagrams) based on recent joint work with Chris Douglas. We focus on three aspects of the theory: (1) the geometric duality of manifold diagrams and pasting diagrams, whose cells provide a novel "universal" class of shapes for higher category theory; (2) how to extend the tantalizing connection between classical singularities and laws of dualizable objects into higher dimensions, overcoming obstructions faced by classical differential singularity theory; and (3) the conjectural "combinatorialization" of smooth structures, which would allow us to faithfully represent smooth structures of manifolds in manifold diagrams, and thus by purely combinatorial means.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Comments: We ask our participants based in the US and Canada to be mindful of the time difference, with the beginning of DST there on March 13th.

Topological Quantum Field Theory Club (IST, Lisbon)

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