On the lexicographic degree of two-bridge knots
نویسندگان
چکیده
We study the degree of polynomial representations of knots. We obtain the lexicographic degree for two-bridge torus knots and generalized twist knots. The proof uses the braid theoretical method developed by Orevkov to study real plane curves, combined with previous results from [KP10] and [BKP14]. We also give a sharp lower bound for the lexicographic degree of any knot, using real polynomial curves properties.
منابع مشابه
Constriction Scour In Pressurized Flow Condition (RESEARCH NOTE)
When depth of flow past a river bridge exceeds opening under the bridge, the flow under the bridge becomes pressurized. The water is directed downward and under the bridge deck, causing increase in velocity and shear stress on the bed thereby increasing bed scour. This is termed as Pressure Flow Scour. The present study investigates the phenomenon of pressure flow scour resulting from a submerg...
متن کاملKnot and Braid Invariants from Contact Homology Ii
We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to embedded graphs and higher-dimensional knots. We calculate the knot invariant for two-bridge knots and relate it to double branched covers for general knots.
متن کاملThe first rational Chebyshev knots
A Chebyshev knot C(a, b, c, φ) is a knot which has a parametrization of the form x(t) = Ta(t); y(t) = Tb(t); z(t) = Tc(t + φ), where a, b, c are integers, Tn(t) is the Chebyshev polynomial of degree n and φ ∈ R. We show that any two-bridge knot is a Chebyshev knot with a = 3 and also with a = 4. For every a, b, c integers (a = 3, 4 and a, b coprime), we describe an algorithm that gives all Cheb...
متن کاملOn Character Varieties of Two-bridge Knot Groups
We find explicit models for the PSL2(C)and SL2(C)-character varieties of the fundamental groups of complements in S of an infinite family of two-bridge knots that contains the twist knots. We compute the genus of the components of these character varieties, and deduce upper bounds on the degree of the associated trace fields. We also show that these knot complements are fibered if and only if t...
متن کاملThe Braid Index and the Growth of Vassiliev Invariants
We use the new approach of braiding sequences to prove exponential upper bounds for the number of Vassiliev invariants on knots with bounded braid index, bounded bridge number and arborescent knots. We prove, that any Vassiliev invariant of degree k is determined by its values on knots with braid index at most k+1.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017