Paper: A brief introduction to framed combinatorial topology

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Date	Comment	Link
Sep 2022	first Draft, pre-arXiv	pdf

Abstract

In this expository note, we give a brief overview of some recently developed ideas in the study of framed combinatorial spaces, and its applications in the definition of manifold diagrams, tame tangles, and the combinatorial study of higher Morse theory.

Idea

This paper gives a brief overview of concepts central to framed combinatorial topology. These concepts include:

• Framed spaces and framed combinatorial spaces
• Meshes and Trusses
• Manifold diagrams and (tame) tangles
• Ideas relating to combinatorial higher Morse Theory

While many details are being glossed over, the idea is that the given details are nonetheless presented in a mathematically self-contained way, in order to provide a minimal working set of definitions for the above concepts.

See also

• Related introductory material
• Related papers