Editing Homotopy groups of spheres (section)

==={{math|π<sub>3</sub>(''S''<sup>2</sup>) {{=}} Z}}===

[[Image:Hopf Fibration.png|right|thumb|The [[Hopf fibration]] is a nontrivial mapping of the 3-sphere to the 2-sphere, and generates the third homotopy group of the 2-sphere. Each colored circle maps to the corresponding point on the 2-sphere shown bottom right.]]

The first nontrivial example with {{math|''i'' > ''n''}} concerns mappings from the [[3-sphere]] to the ordinary 2-sphere, and was discovered by [[Heinz Hopf]], who constructed a nontrivial map from {{math|''S''<sup>3</sup>}} to {{math|''S''<sup>2</sup>}}, now known as the [[Hopf fibration]].{{sfn|Hopf|1931}} This map [[Generating set of a group|generates]] the homotopy group {{math|π<sub>3</sub>(''S''<sup>2</sup>) {{=}} Z}}.{{sfn|Walschap|2004|p=90}}