Affiliation:
1. Department of Mathematics, Nara National College of Technology, Yata-cho 22, Yamatokoriyama, Nara 639-1080, Japan
Abstract
For an arbitrary 1-knot k1, the spun 2-knot of k1, denoted by spun (k1), is a ribbon 2-knot in R4. Hence for a ribbon 2-knot K2, we can also induce a notion corresponding to the crossing number on a 1-knot, and it is said to be the crossing number of K2, denoted by cr (K2). In this note, we will show that the Alexander polynomial plays an important role in determining the crossing number of a ribbon 2-knot. Lastly, we will prove the following: If k1is a (p,q)-torus knot, then cr ( spun (k1)) is equal to (p - 1)(q - 1).
Publisher
World Scientific Pub Co Pte Lt
Subject
Algebra and Number Theory
Cited by
5 articles.
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