Download Padic Homotopy Theory

p-adic homotopy theory
There should be p-adic homotopy theories for every
prime p analogous to Sullivan’s Real homotopy theory.
A norm on Q induces a unique topology on any finite
dimensional vector V space over Q; hence V determines
Vp a finite dimensional topological vector space over Qp.
If V is infinite dimensional, then use the direct limit of
Wp, where W is a finite dimensional subspace of V. If X
is a simplicial set and QX={QsX} is the Bousfield-Kan
rational homotopy type, then define QpX to be the
inverse system of Qp topological vector spaces obtained
from QX. This is my proposed definition of p-adic
homotopy theory.