Orbit space
Properties

Orbit space

Given a group $𝐺$ acting on a space $𝑋$ , the orbit space¹ or quotient $𝑋 / 𝐺$ is the set of orbits partitioning $𝑋$ . group If $𝑋$ is a topological space, $𝑋 / 𝐺$ is typically endowed with the quotient topology induced by the projection $𝑝 : 𝑥 \mapsto 𝐺 𝑥$ .

Properties

The Orbit space of a properly discontinuous group action $𝑋 / 𝐺$ is a covered by $𝑋$

tidy | en | SemBr

Footnotes

German Bahnenraum. ↩

Graph View

Backlinks

Braid group
Correspondence between regular coverings and orbit spaces of their deck transformation groups
Group action orbit
Group action
Homogenous coördinates
Main theorem of coverings
Orbit space of a properly discontinuous effective group action
Orbit space of a properly discontinuous group action
Projectivization

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