English

Hypercovers in topology

Algebraic Topology 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0111287,
  title  = {Hypercovers in topology},
  author = {Daniel Dugger and Daniel C. Isaksen},
  journal= {arXiv preprint arXiv:math/0111287},
  year   = {2007}
}

Comments

20 pages