Algebraic homotopy classes of rational functions
Algebraic Topology
2009-12-23 v2 Algebraic Geometry
Abstract
We compute the set of naive pointed homotopy classes of endomorphisms of the projective line P^1 over the spectrum of a field. Our computation compares well with Fabien Morel's one of the motivic pointed homotopy classes of endomorphisms of P^1: there is an a priori monoid structure on the set of naive homotopy classes such that canonical map from this monoid to group of motivic homotopy classes is a group completion.
Keywords
Cite
@article{arxiv.0912.2227,
title = {Algebraic homotopy classes of rational functions},
author = {Christophe Cazanave},
journal= {arXiv preprint arXiv:0912.2227},
year = {2009}
}
Comments
30 pages; Improved the comparison between naive and motivic homotopy classes. Added one appendix