Academic Journal
The $C$–polynomial of a knot
| العنوان: | The $C$–polynomial of a knot |
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| المؤلفون: | Garoufalidis, Stavros, Sun, Xinyu |
| بيانات النشر: | MSP |
| سنة النشر: | 2006 |
| المجموعة: | Project Euclid (Cornell University Library) |
| مصطلحات موضوعية: | WZ algorithm, creative telescoping, colored Jones function, Gosper's algorithm, cyclotomic function, holonomic functions, characteristic varieties, $A$-polynomial, $C$-polynomial, 57N10, 57M25 |
| الوصف: | In an earlier paper the first author defined a non-commutative [math] –polynomial for knots in 3–space, using the colored Jones function. The idea is that the colored Jones function of a knot satisfies a non-trivial linear [math] –difference equation. Said differently, the colored Jones function of a knot is annihilated by a non-zero ideal of the Weyl algebra which is generalted (after localization) by the non-commutative [math] –polynomial of a knot. ¶ In that paper, it was conjectured that this polynomial (which has to do with representations of the quantum group [math] ) specializes at [math] to the better known [math] –polynomial of a knot, which has to do with genuine [math] representations of the knot complement. ¶ Computing the non-commutative [math] –polynomial of a knot is a difficult task which so far has been achieved for the two simplest knots. In the present paper, we introduce the [math] –polynomial of a knot, along with its non-commutative version, and give an explicit computation for all twist knots. In a forthcoming paper, we will use this information to compute the non-commutative [math] –polynomial of twist knots. Finally, we formulate a number of conjectures relating the [math] , the [math] –polynomial and the Alexander polynomial, all confirmed for the class of twist knots. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 1472-2747 1472-2739 |
| Relation: | https://projecteuclid.org/euclid.agt/1513796600; Algebr. Geom. Topol. 6, no. 4 (2006), 1623-1653 |
| DOI: | 10.2140/agt.2006.6.1623 |
| الاتاحة: | https://projecteuclid.org/euclid.agt/1513796600 https://doi.org/10.2140/agt.2006.6.1623 |
| Rights: | Copyright 2006 Mathematical Sciences Publishers |
| رقم الانضمام: | edsbas.53856E95 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 14722747 14722739 |
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| DOI: | 10.2140/agt.2006.6.1623 |