A simplicial model for the Hopf map
Algebraic Topology
2007-05-23 v1
Abstract
We give an explicit simplicial model for the Hopf map S^3 -> S^2. For this purpose, we construct a model of S^3 as a principal twisted cartesian product K x_{eta} S^2, where K is a simplicial model for S^1 acting by left multiplication on itself, S^2 is given the simplest simplicial model and the twisting map is eta:(S^2)_n -> (K)_{n-1}. We construct a Kan complex for the simplicial model K of S^1. The simplicial model for the Hopf map is then the projection K x_{eta} S^2 -> S^2.
Cite
@article{arxiv.math/0310456,
title = {A simplicial model for the Hopf map},
author = {Orin R. Sauvageot},
journal= {arXiv preprint arXiv:math/0310456},
year = {2007}
}