Covering

Regular covering

A regular covering is a covering for which the characteristic subgroup is basepoint-invariant 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

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Footnotes

1. If this holds for one basepoint it holds for all basepoints, see Characteristic conjugacy class of a path-connected covering ↩