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A simplicial model for the Hopf map

Orin R. Sauvageot

math.ATarXiv:math/0310456

Abstract

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.

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