nLab Riemann sphere

Contents

Context

Spheres

n-sphere

low dimensional n-spheres

complex geometry

Contents

Idea

The 2-sphere with its canonical structure of a complex manifold is called the Riemann sphere.

As such this is complex projective space $\mathbb{C}P^1$.

Properties

The biholomorphisms, i.e. the bijective conformal transformations from the Riemann sphere to itself are the Möbius transformations.

References

See also

On the homotopy type of the space of rational functions from the Riemann sphere to itself (related to the moduli space of monopoles in $\mathbb{R}^3$ and to the configuration space of points in $\mathbb{R}^2$):

Last revised on August 4, 2020 at 09:03:00. See the history of this page for a list of all contributions to it.