1. A theory of genera for cyclic coverings of links
- Author
-
Masanori Morishita
- Subjects
Discrete mathematics ,Rational number ,Pure mathematics ,General Mathematics ,Gauss ,Field (mathematics) ,Algebraic number field ,genus and central class coverings ,Mathematics::Geometric Topology ,11R ,Knot theory ,57M12 ,Knot invariant ,Line (geometry) ,57M25 ,Arithmetic function ,genera of homology classes ,Links ,Mathematics - Abstract
Following the conceptual analogies between knots and primes, 3-manifolds and number fields, we discuss an analogue in knot theory after the model of the arithmetical theory of genera initiated by Gauss. We present an analog for cyclic coverings of links following along the line of Iyanaga-Tamagawa's genus theory for cyclic extentions over the rational number field. We also give examples of $\mathbf{Z} / 2\mathbf{Z} \times \mathbf{Z} / 2\mathbf{Z}$-coverings of links for which the principal genus theorem does not hold.
- Published
- 2001