2 5 M ay 2 00 9 Any smooth knot S n →֒ R n + 2 is isotopic to a cubic knot contained in the canonical scaffolding of R n + 2 ∗
نویسندگان
چکیده
The n-skeleton of the canonical cubulation C of R into unit cubes is called the canonical scaffolding S. In this paper, we prove that any smooth knot can be continuously isotoped by an ambient isotopy of R to a knot contained in S.
منابع مشابه
ar X iv : g r - qc / 0 21 00 36 v 1 1 1 O ct 2 00 2 LINKING , LEGENDRIAN LINKING AND CAUSALITY
The set N of all null geodesics of a globally hyperbolic (d + 1)-dimensional spacetime (M, g) is naturally a smooth (2d − 1)-dimensional contact manifold. The sky of an event x ∈ M is the subset X = {γ ∈ N : x ∈ γ} ⊂ N and is an embedded Legendrian submanifold of N diffeomorphic to S d−1. It was conjectured by Low that for d = 2 events x, y ∈ M are causally related iff X, Y ⊂ N are linked (in a...
متن کاملA Note on Knot Invariants In
We prove a relation between several easy-to-define numerical invariants of generic knots in H × S, and discuss its implication to contact geometry. 1. Definitions of Invariants The 2-dimensional hyperbolic space H2 is defined to be the upper half plane {(x, y) ∈ R2| y > 0} equipped with the metric ds2 = dx +dy y2 . STH2 is the unit tangent bundle of H2, i.e., the S1-bundle over H2 formed by tan...
متن کاملar X iv : 0 90 8 . 01 53 v 1 [ m at h . G T ] 2 A ug 2 00 9 On Fibonacci knots
We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when n 6≡ 0 (mod 4) and (n, j) 6= (3, 3), the Fibonacci knot F (n) j is not a Lissajous knot. keywords: Fibonacci polynomials, Fibonacci knots, continued fractions
متن کاملMore 3-manifolds with multiple knot-surgery and branched-cover descriptions
For any integer N ^ 3 we will construct a 3-manifold which can be described as +1 surgery on N distinct knots in S. We will also give examples of 3-manifolds which are i^-fold cyclic branched covers of S over 2 distinct knots. Brakes (2) discovered the first examples of 3-manifolds with multiple knot surgery descriptions. Our construction is much different and follows directly from the construc...
متن کاملThere Exist Non-trivial Pl Knots Whose Complements Are Homotopy Circles
We show that there exist non-trivial PL knots S n−2 ⊂ S n , n ≥ 5, whose complements have the homotopy type of circles. This is in contrast to the case of smooth, PL locally-flat, and topological locally-flat knots, for which it is known that if the complement has the homotopy type of a circle, then the knot is trivial. It is well-known that if the complement of a smooth, PL locally-flat, or to...
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 2009