Volume Bounds for Weaving Knots

نویسندگان

  • ABHIJIT CHAMPANERKAR
  • J. PURCELL
  • Xiao-Song Lin
چکیده

Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically correct volume bounds for weaving knots, and we prove that the infinite weave is their geometric limit.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

p-Colorings of Weaving Knots

We explore the p-colorability of a family of knots known as weaving knots. First, we show some general results pertaining to p-coloring any (m, n) weaving knot. We then determine the p-colorability of any (m, 3) weaving knot, and designate these p-colorings into two separate types, whose characteristics we begin to explore. We also partially classify some of the p-colorings for any (m, n) weavi...

متن کامل

Plain Woven Objects

Article Submission For inclusion in Hyperseeing, authors are invited to email articles for the preceding categories to: Articles should be a maximum of eight pages. Plain weaving is one of the most beautiful and widely used geometric forms. In plain weaving, a set of distinct threads (or yarns) are interlaced with each other to form a fabric or cloth where each thread crosses the other threads ...

متن کامل

On Diagrammatic Bounds of Knot Volumes and Spectral Invariants

In recent years, several families of hyperbolic knots have been shown to have both volume and λ1 (first eigenvalue of the Laplacian) bounded in terms of the twist number of a diagram, while other families of knots have volume bounded by a generalized twist number. We show that for general knots, neither the twist number nor the generalized twist number of a diagram can provide two–sided bounds ...

متن کامل

Volume Bounds for Generalized Twisted Torus Links

Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their hyperbolic volumes that depend only on the number of strands being twisted. W...

متن کامل

Geometrically and diagrammatically maximal knots

The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural question motivated by these bounds: For which knots are these ratios nearly maximal? We show that many families of alternating knots and links simultaneously maximi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015