Abstract and PDF downloads
Upon observing an apparant inductive structure in some (heuristic, but not formalized) idea of what manifold diagrams should be, I wrote out the combinatorial theory of “singular cubes”. The theory of these combinatorial structures is excitingly rich and a lot of things just work nicely, which led to the thesis “writing itself” and resulted in a rather long document (one may argue that this is also due to me writing out all calculations and verifications in quite a lot of (…way too much) detail). The theory was subsequently generalized in absorbed into the theory of “trusses” developed with Christopher Douglas, based on the realization that, really, “framed combinatorial-topological models” should use the duals of the structures considered in my thesis. See the book for more details, and a paper that makes the underlying intuition about manifold diagrams formal.
There are (at least) a couple of claims that are wrong. I’ll hope to eventually write out a list of issues here.