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Sur le polynôme de Jones modulaire.
- Source :
-
Comptes Rendus. Mathématique . 2020, Vol. 358 Issue 8, p901-908. 8p. - Publication Year :
- 2020
-
Abstract
- A major problem in knot theory is to decide whether the Jones polynomial detects the unknot. In this paper we study a weaker related problem, namely whether the Jones polynomial reduced modulo an integer m detects the unknot. The answer is known to be negative for m = 2r with r ≥ 1 and m = 3. Here we show that if the answer is negative for some m, then it is negative for mr with any r ≥ 1. In particular, for any r ≥ 1, we construct nontrivial knots whose Jones polynomial is trivial modulo 3r. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MODULAR arithmetic
*INTEGERS
*POLYNOMIALS
*KNOT theory
Subjects
Details
- Language :
- French
- ISSN :
- 1631073X
- Volume :
- 358
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Comptes Rendus. Mathématique
- Publication Type :
- Academic Journal
- Accession number :
- 160055502
- Full Text :
- https://doi.org/10.5802/crmath.106