A simplicial model for the Hopf map

Details A simplicial model for the Hopf map A simplicial model for the Hopf map

2003-10-29

arxiv.org/abs/math/0310456v1

Mathematics

Algebraic Topology

Scientific paper

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.

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