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 may induce a cyclic Galois covering with cyclic group of order .