紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2010, 47(4), p. 977-1027

Rational Witt classes of pretzel knots

Jabuka, Stanislav

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2010-12

In his two pioneering articles [9, 10] Jerry Levine introduced and completely determined the algebraic concordance groups of odd dimensional knots. He did so by defining a host of invariants of algebraic concordance which he showed were a complete set of invariants. While being very powerful, these invariants are in practice often hard to determine, especially for knots with Alexander polynomials of high degree. We thus propose the study of a weaker set of invariants of algebraic concordance—the rational Witt classes of knots. Though these are rather weaker invariants than those defined by Levine, they have the advantage of lending themselves to quite manageable computability. We illustrate this point by computing the rational Witt classes of all pretzel knots. We give many examples and provide applications to obstructing sliceness for pretzel knots. Also, we obtain explicit formulae for the determinants and signatures of all pretzel knots. This article is dedicated to Jerry Levine and his lasting mathematical legacy; on the occasion of the conference “Fifty years since Milnor and Fox” held at Brandeis University on June 2–5, 2008.

10.18910/4337

4337

Rational Witt classes of pretzel knots

Jabuka, Stanislav

Osaka University and Osaka City University, Departments of Mathematics

英語

2010-12

Osaka Journal of Mathematics

47

4

977

1027

https://hdl.handle.net/11094/4337

10.18910/4337

https://doi.org/10.18910/4337