Knots and links in spatial graphs

نویسنده

  • Kouki Taniyama
چکیده

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 general. For example Kinoshita’s theta curve in Fig. 1 is not trivial but contains only trivial knots as the trivial theta curve. See for other such examples [5], [20] and [15].

برای دانلود رایگان 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

Spatial graphs with local knots

It is shown that for any locally knotted edge of a 3-connected graph in S^3, there is a ball that contains all of the local knots of that edge and it is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in S^3. Response to Reviewers: See attachment. SPATIAL GRAPHS WITH LOCAL KNOTS ERICA FLAPAN, BLAKE MELLOR, A...

متن کامل

On Chirality of Toroidal Embeddings of Polyhedral Graphs

We investigate properties of spatial graphs on the standard torus. It is known that nontrivial embeddings of planar graphs in the torus contain a nontrivial knot or a nonsplit link due to [1],[2]. Building on this and using the chirality of torus knots and links [3],[4], we prove that nontrivial embeddings of simple 3connected planar graphs in the standard torus are chiral. For the case that th...

متن کامل

Self-Linking Invariant of Virtual Knots

This paper introduces a self-linking invariant for virtual knots and links, and relates this invariant to a state model called the binary bracket, and to a class of coloring problems for knots and links that include classical coloring problems for cubic graphs. (AMS Subject Classification Number 57M27)

متن کامل

Knots and links in spatial graphs

The main purpose of this paper is to show that any embedding of K7 in three-dimensional euclidean space contains a knotted cycle. By a similar but simpler argument, it is also shown that any embedding of K, contains a pair of disjoint cycles which are homologically linked.

متن کامل

Polyhedral Knots and Links

This paper contains a survey of different methods for generating knots and links based on geometric polyhedra, suitable for applications in chemistry, biology, architecture, sculpture (or jewelry). We describe several ways of obtaining 4-valent polyhedral graphs and their corresponding knots and links from geometrical polyhedra: midedge construction, cross-curve and double-line covering, and ed...

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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002