Category of coverings

Deck transformation

A deck transformation¹ of a covering is an automorphism of in Category of coverings.² homotopy The set of all deck transformations is clearly a subgroup of the group of homeomorphisms of , called the deck transformation group³. The deck transformation group has a natural group action on the covering space by application.

Properties

• A covering is regular iff its deck transformation group acts transitively on fibres
• A deck transformation maps sheets to sheets
• The deck transformation group acts properly discontinuously

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Footnotes

1. German Decktransformation ↩

2. 2010, Algebraische Topologie, p. 95 ↩

3. German Decktransformationsgruppe ↩