Christoph Dorn

Mathematician and computer scientist. Interested in computable foundations of geometry and higher algebra.

Framed Combinatorial Topology

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology and higher algebra.

Here’s a page that collects basic ideas and material about the subject.

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The $D_4$ dualizability law

Comments first published

This notes gives a brief visual guide to how one can understand the classical \(D_4\) singularity in terms of a categorical pasting diagrams (aka manifold diagram, or more specifically, a tame tangle). → read note

The categorical Pontryagin-Thom construction

Comments first published

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