When a university says they research in "combinatorial topology" what does that mean?
I've seen a university in Country A list "combinatorial topology" in its math department's research areas, but I cannot find a professor who researches "combinatorial topology" or any course offered by the university under the name "combinatorial topology".
"Combinatorial topology" does not refer to "algebraic topology" because the university's math department has a course "algebraic topology", and "algebraic topology" is listed in the research interests.
I could email the university, but I'm asking in general so I won't have to email every university
What "combinatorial topology" does Munkres Topology cover?
I think Section 64 "Imbedding Graphs in the Plane" and all of Chapter 14 are "combinatorial" because they involve graphs.
My idea of "combinatorial topology" based on my 1 course on discrete mathematics 8 years ago and 1 my course on operations research 2 years ago and based on the Wikipedia "See also" for Combinatorial topology is "topological combinatorics" or "topological graph theory". Therefore, when I see "graphs" (as in "vertices" and "edges") in this textbook, I think it is combinatorial topology.
Also, based on the Wikipedia page for Topological graph theory, I think this is exactly what is covered in Chapter 14 wherein graphs are seen as topological spaces which are unions of arcs, spaces homeomorphic to $[0,1]$.
- What are some "combinatorial topology" textbooks?
I think numbers 1 and 2 are answered if 3 is answered.