I gave a talk at CUNY about factorization homology, and have written up some notes which I’m posting here.
You May Also Enjoy
The Pontryagin-Thom construction is a deep relation between smooth manifold theory and homotopy theory. We use the language of manifold diagrams and computads to give a purely combinatorial perspective on the construction. On our way, we’ll discuss computadic functors and transformations, and how the combinatorics of manifold diagrams may provide a “combinatorialization” of smooth structures on manifolds altogether. → read note
This note gives a fast introduction to the rich combinatorial theory of trusses. We also discuss how presheafs of truss blocks give rise to weak computads, and how this can be used to understand manifold diagrams in purely combinatorial terms. → read note
Classical singularity theory and higher category theory have tantalizing connections: via the generalized tangle hypothesis we can understand singularities as expressing categorical laws satisfied by dualizable objects. However, classical singularity theory, based in differential-topological foundations, encounters technical problem in higher dimensions, which stalls this connection. Using our technology of manifold diagrams we outline steps towards remedying the problem, paving the way towards “higher” Morse theory. → read note
Most models for higher categories are based on the paradigm of contractibility; this requires spaces of evaluations of a single pasting diagram to be contractible. The paradigm, however, generally fails to yield easy descriptions of interesting non-contractible behaviour in spaces of composites. To remedy this, we discuss the paradigm of homotopicity. → read note