Regular covering

A regular covering is a covering $𝑝 : ˜ 𝑋 ↠ 𝑋$ for which the characteristic subgroup is basepoint-invariant #m/def/homotopy or equivalently, the characteristic subgroup¹ is normal.

Properties

Note that many of these properties are restricted to connected and path-connected regular coverings.

Deck transformation group of a regular covering as quotient
A covering is regular iff its deck transformation group acts transitively on fibres
Correspondence between regular coverings and orbit spaces of their deck transformation groups

#state/develop | #lang/en | #SemBr

If this holds for one basepoint $˜ 𝑥 0$ it holds for all basepoints, see Characteristic conjugacy class of a path-connected covering ↩

Regular covering

Properties

Footnotes