Hypercovers in topology, by Daniel Dugger and Daniel C. Isaksen

We show that if U is a hypercover of a topological space X then the natural map from hocolim U to X is a weak equivalence. This fact is used to construct topological realization functors for the A^1-homotopy theory of schemes over real and complex fields.

Daniel Dugger <ddugger@math.purdue.edu>
Daniel C. Isaksen <isaksen.1@nd.edu>