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.^[1]^[2] As with cyclic groups, there may be both finite and infinite cyclic covers.^[3]

Cyclic covers have proven useful in the descriptions of knot topology^[1]^[3] and the algebraic geometry of Calabi–Yau manifolds.^[2]

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.^[4] 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 $r$ .

References

^ ^a ^b Seifert and Threlfall, A Textbook of Topology. Academic Press. 1980. p. 292. ISBN 9780080874050. Retrieved 25 August 2017. cyclic covering.
^ ^a ^b Rohde, Jan Christian (2009). Cyclic coverings, Calabi-Yau manifolds and complex multiplication ([Online-Ausg.]. ed.). Berlin: Springer. pp. 59–62. ISBN 978-3-642-00639-5.
^ ^a ^b Milnor, John. "Infinite cyclic coverings" (PDF). Conference on the Topology of Manifolds. Vol. 13. 1968. Retrieved 25 August 2017.
^ Ambro, Florin (2013). "Cyclic covers and toroidal embeddings". arXiv:1310.3951 [math.AG].

References

Further reading