Profinite homotopy theory

By Gereon Quick. Documenta Mathematica, 2008

48 citations recorded by the source corpus.

We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite struc- ture. This yields a rigid profinite completion functor for spaces and pro-spaces. One motivation is thehomotopy theory of schemes in which higher profiniteetale homotopy groups fit well with the ´ fundamental group which is always profinite. We show that the profi- nitetopological realization functor is a good object in several respects.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/16b24cdeeb57b29e6fb2c864056fdd877b991fc6