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Homotopy theory, homological algebra, algebraic treatments of manifolds.

4 votes
3 answers
526 views

reference for the cubical structure of the associahedra

I cannot find where I learned that the $n$-dimensional associahedron is a union of $n$-cubes. The vertices of the $n$-dimensional associahedron are the finite binary trees having $n+2$ leaves and the …
Matt Brin's user avatar
  • 1,625
10 votes
2 answers
684 views

Symmetries and faces of the associahedron

The dihedral group of order $2n+2$ acts on $K_n$, the ($n-2$)-dimensional associahedron. Are there any other symmetries? References? Does the answer to 1 change if we restrict to just the 1-skelet …
Matt Brin's user avatar
  • 1,625
8 votes

Different way to view action of fundamental group on higher homotopy groups

I doubt this would be considered less geometric than the actions in your question, but if $(X,x_0)$ has a universal cover with covering map $p:(\tilde X, \tilde x_0)\rightarrow (X,X_0)$, then $p$ indu …
Matt Brin's user avatar
  • 1,625