Mirror-curve Codes for Knots and Links

نویسندگان

  • Ljiljana Radović
  • Slavik Jablan
چکیده

Inspired by Lomonaco–Kauffman paper on quantum knots and knot mosaics we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. We introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grid, suitable for software implementations and discuss possible applications of mirror-curves.

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

Virtual Knot Theory

This paper is an introduction to the subject of virtual knot theory, a generalization of classical knot theory that I discovered in 1996 [2]. This paper gives the basic definitions, some fundamental properties and a collection of examples. Subsequent papers will treat specific topics such as classical and quantum link invariants and Vassiliev invariants for virtual knots and links in more detai...

متن کامل

Knots in Art

We analyze applications of knots and links in the Ancient art, beginning from Babylonian, Egyptian, Greek, Byzantine and Celtic art. Construction methods used in art are analyzed on the examples of Celtic art and ethnical art of Tchokwe people from Angola or Tamil art, where knots are constructed as mirror-curves. We propose different methods for generating knots and links based on geometric po...

متن کامل

ar X iv : h ep - p h / 04 08 02 5 v 1 3 A ug 2 00 4 Universal energy spectrum of tight knots and links in physics ∗

It is known from plasma physics that linked magnetic flux tubes are much more stable than an unknotted single loop [1]. Linked flux tubes carry topological charge, and this can be thought of as a conserved (at least to lowest order) physical quantum number. Similarly, knotted flux tubes carry topological quantum numbers, and one can think of a knot as a self-linked loop. The topological charges...

متن کامل

Knots and links in spatial graphs

We study the relations of knots and links contained in a spatial graph. This is an survey article on the results about knots and links contained in a spatial graph. We do not intend to cover all results in this topic. We only treat some of them here. The set of knots and links contained in a spatial graph is a naive invariant of spatial graph. However it is of course not a complete invariant in...

متن کامل

Quandle colorings of knots and applications.

We present a set of 26 finite quandles that distinguish (up to reversal and mirror image) by number of colorings, all of the 2977 prime oriented knots with up to 12 crossings. We also show that 1058 of these knots can be distinguished from their mirror images by the number of colorings by quandles from a certain set of 23 finite quandles. We study the colorings of these 2977 knots by all of the...

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 2013