منابع مشابه
Is the Jones Polynomial of a Knot Really a Polynomial?
The Jones polynomial of a knot in 3-space is a Laurent polynomial in q, with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing definitions of the Jones polynomial, we show that the Jones polynomial is really an ...
متن کاملCompleting a Polynomial Knot from a Projection
Given a knot-type and a projection of it parameterized by two polynomials we can find a third polynomial that will form a representation of the knot in R along with the two given polynomials. This paper discusses methods with which to find this third polynomial and some related results.
متن کاملThe C-polynomial of a knot
We derive, from the A-polynomial of a knot, a single variable polynomial for the knot, called C-polynomial, and explore topological and geometrical information about the knot encoded in the C-polynomial. 2003 Elsevier B.V. All rights reserved. MSC: 57N10; 57M25; 57M27; 57M40
متن کاملThe Knot Group and The Jones Polynomial
In this thesis, basic knot theory is introduced, along with concepts from topology, algebra and algebraic topology, as they relate to knot theory. In the first chapter, basic definitions concerning knots are presented. In the second chapter, the fundamental group is applied as a method of distinguishing knots. In particular the torus knots are classified using the fundamental group, and a gener...
متن کاملFree Knot Polynomial Spline Confidence Intervals
We construct approximate confidence intervals for a nonparametric regression function. The construction uses polynomial splines with free knot locations. The number of knots is determined by the GCV criteria. The estimates of knot locations and coefficients are obtained through a nonlinear least square solution that corresponds to the maximum likelihood estimate. Confidence intervals are then c...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14166