cyclic cover

In algebraic topology and algebraic geometry, a cyclic cover or cyclic covering is a covering space for which the set of covering transformations forms a cyclic group.{{cite book|title=Seifert and Threlfall, A Textbook of Topology|date=1980|publisher=Academic Press|isbn=9780080874050|page=[https://archive.org/details/seifertthrelfall0000seif/page/292 292]|url=https://archive.org/details/seifertthrelfall0000seif|url-access=registration|quote=cyclic covering.|accessdate=25 August 2017|language=en}}{{cite book|last1=Rohde|first1=Jan Christian|title=Cyclic coverings, Calabi-Yau manifolds and complex multiplication|date=2009|publisher=Springer|location=Berlin|isbn=978-3-642-00639-5|pages=59–62|edition=[Online-Ausg.].}} As with cyclic groups, there may be both finite and infinite cyclic covers.{{cite web|last1=Milnor|first1=John|title=Infinite cyclic coverings|url=http://www.maths.ed.ac.uk/~aar/papers/milncycl.pdf|publisher=Conference on the Topology of Manifolds. Vol. 13. 1968.|accessdate=25 August 2017}}

Cyclic covers have proven useful in the descriptions of knot topology and the algebraic geometry of Calabi–Yau manifolds.

In classical algebraic geometry, cyclic covers are a tool used to create new objects from existing ones through, for example, a field extension by a root element.{{cite arXiv |eprint=1310.3951|last1=Ambro|first1=Florin|title=Cyclic covers and toroidal embeddings|class=math.AG|year=2013}} The powers of the root element form a cyclic group and provide the basis for a cyclic cover. A line bundle over a complex projective variety with torsion index $r$ may induce a cyclic Galois covering with cyclic group of order $r$.