2003/10/29 by Orin R. Sauvageot, Sauvageot, Orin R.
Mathematics · #55Q40 #55R10 #55U10 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55Q40 #msc:55R10 #msc:55U10
paper · pdf · doi:10.48550/arxiv.math/0310456
arxiv created 2003/10/29 · arxiv updated 2009/12/01
We give an explicit simplicial model for the Hopf map S3 -> S2. For this purpose, we construct a model of S3 as a principal twisted cartesian product K xeta S2, where K is a simplicial model for S1 acting by left multiplication on itself, S2 is given the simplest simplicial model and the twisting map is eta:(S2)n -> (K)n-1. We construct a Kan complex for the simplicial model K of S1. The simplicial model for the Hopf map is then the projection K xeta S2 -> S2.