From Wikipedia, the free encyclopedia

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 .

References

  1. ^ a b Seifert and Threlfall, A Textbook of Topology. Academic Press. 1980. p.  292. ISBN  9780080874050. Retrieved 25 August 2017. cyclic covering.
  2. ^ 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.
  3. ^ a b Milnor, John. "Infinite cyclic coverings" (PDF). Conference on the Topology of Manifolds. Vol. 13. 1968. Retrieved 25 August 2017.
  4. ^ Ambro, Florin (2013). "Cyclic covers and toroidal embeddings". arXiv: 1310.3951 [ math.AG].

Further reading


From Wikipedia, the free encyclopedia

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 .

References

  1. ^ a b Seifert and Threlfall, A Textbook of Topology. Academic Press. 1980. p.  292. ISBN  9780080874050. Retrieved 25 August 2017. cyclic covering.
  2. ^ 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.
  3. ^ a b Milnor, John. "Infinite cyclic coverings" (PDF). Conference on the Topology of Manifolds. Vol. 13. 1968. Retrieved 25 August 2017.
  4. ^ Ambro, Florin (2013). "Cyclic covers and toroidal embeddings". arXiv: 1310.3951 [ math.AG].

Further reading



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