Are there p-adic knot invariants?

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• 作者：A. Yu. Morozov
• 刊名：Theoretical and Mathematical Physics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：187
• 期：1
• 页码：447-454
• 全文大小：429 KB
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mathematical and Computational Physics
  Applications of Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9333
• 卷排序：187

文摘

We suggest using the Hall–Littlewood version of the Rosso–Jones formula to define the germs of p-adic HOMFLY-PT polynomials for torus knots [m, n] as coefficients of superpolynomials in a q-expansion. In this form, they have at least the [m, n] ↔ [n, m] topological invariance. This opens a new possibility to interpret superpolynomials as p-adic deformations of HOMFLY polynomials and poses a question of generalizing to other knot families, which is a substantial problem for several branches of modern theory.Keywordsknot polynomialp-adic analysisp-adic string