7
votes
4answers
502 views

Knot diagrams, sets of moves and equivalence relations

Short version: Does anyone study equivalence classes generated by a given set of "moves" (in the sense of, but not limited to, Reidemeister moves) on the set of knot diagrams? Yes, I understand that ...
6
votes
0answers
420 views

Historical and terminological questions about Dan Kan's Ex functor and its relation to the classical case of simplicial complexes

Recall that we may define a functor $\xi:\Delta\to \operatorname{Poset}$ sending a simplex $[n]$ to the set of monotone injections $[k]\hookrightarrow [n]$ for $k\geq 0$ (effectively, $k\leq n$ as ...
14
votes
3answers
2k views

Why is complex projective space triangulable?

In an exercise in his algebraic topology book, Munkres asserts that $\mathbf{C}P^n$ is triangulable (i.e., there is a simplicial complex $K$ and a homeomorphism $|K| \rightarrow \mathbf{C}P^n$). Can ...
4
votes
1answer
687 views

The Join of Simplicial Sets ~Finale~

Background Let $X$ and $S$ be simplicial sets, i.e. presheaves on $\Delta$, the so-called topologist's simplex category, which is the category of finite nonempty ordinals with morphisms given by ...