nLab 2-sphere

Idea

The 2-sphere $S^2$ is the ordinary sphere of dimension $2$, hence the $n$-sphere for $n = 2$.

Equipped with its canonical complex structure this is known as the Riemann sphere.

Related concepts

• geometric quantization of the 2-sphere

• spherical braid group

References

General

• Wikipedia: Sphere

• Wikipedia: 2-sphere

Loop space of the 2-sphere

On the loop space $\Omega S^2$ of the 2-sphere

in relation to braid groups

• Frederick R. Cohen, J. Wu: On Braid Groups, Free Groups, and the Loop Space of the 2-Sphere, in: Categorical Decomposition Techniques in Algebraic Topology, in Progress in Mathematics 215, Birkhäuser (2003) 93-105 [doi:10.1007/978-3-0348-7863-0_6]

and regarded as a classifying space, $\Omega S^2 \,\simeq\, B \Omega^2 S^2$, (for “$\mathbf{l}$ine” bundles in nonabelian cohomology):

• Jack Morava: A homotopy-theoretic context for CKM/Birkhoff renormalization [arXiv:2307.10148, spire:2678618]

• Jack Morava: Some very low-dimensional algebraic topology [arXiv:2411.15885]