nLab spheres -- contents

n-sphere

• unit sphere, polar coordinates

• round sphere, squashed sphere

• hemisphere, equator

• stereographic projection

• homotopy groups of spheres

• homotopy sphere, rational homotopy sphere, Cohomotopy

• spherical fibration, twisted Cohomotopy

• sphere spectrum, stable Cohomotopy theory

• homology sphere

• rational homotopy sphere, rational n-sphere

• motivic sphere

• group actions on spheres

• representation sphere, equivariant Cohomotopy

• Reeb sphere theorem

• sphere packing

• Music of the Spheres

low dimensional n-spheres

• circle

  • real projective space$\,\mathbb{R}P^1$

• 2-sphere

  • complex projective line$\,\mathbb{C}P^1$: Riemann sphere

  • geometric quantization of the 2-sphere

  • fuzzy 2-sphere

• 3-sphere

  • fuzzy 3-sphere

• 4-sphere

  • quaternionic projective line$\,\mathbb{H}P^1$

  • fuzzy 4-sphere

• 5-sphere

• 6-sphere

• 7-sphere

  • exotic 7-sphere

• 8-sphere

  • octonionic projective line$\,\mathbb{O}P^1$

• 13-sphere

• 15-sphere

• infinite-dimensional sphere