Book: Framed combinatorial topology

Comments first published

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The idea of the book is provide an entry point to (combinatorial) stratified geometry in directed or ‘framed’ spaces (see, for instance, manifold diagrams) from a perspective of classical combinatorial topology. That is, the book starts out with well-known classical combinatorial-topological concepts (such as simplices and regular cells) and builds on these to define framing and stratification structures.

The book roughly contains:

  • Ch. 1 : discussion of framed combinatorial-topological structures based on the idea of “affine framed combinatorics”
  • Ch. 2 - 3 : classification of framed regular cells via the theory of trusses
  • Ch. 4 - 5 : discussion local, framed, stratifed structures
  • App. A: linear algebraic discussion of “metric-free orthonormal frames”
  • App. B: review of elementary notions in stratified topology

It does not contain:

  • An in-depth discussion of global framed combinatorial-topological spaces
  • Higher Category Theory

Incomplete to-do list

  • … fix more mistakes :-)

See also