Note: This page is part of

where you’ll find many more pictures of knots and links as well as MPEG animations and lots of things to download.The KnotPlot Site,

Knot theory is a branch of algebraic topology where one studies what is known as the placement problem, or the embedding of one topological space into another. The simplest form of knot theory involves the embedding of the unit circle into three-dimensional space. For the purposes of this document a knot is defined to be a closed piecewise linear curve in three-dimensional Euclidean space R Two knots or links are considered equivalent if one can be smoothly deformed into the other, or equivalently, if there exists a The simplest non-trivial knot is the trefoil knot which comes in a left and a right handed form.
It is not too difficult to see (but slightly more difficult to prove) that the trefoil is not equivalent to the unknot. Also, the right and left handed versions of the trefoil are only equivalent if the homeomorphism mapping one into the other includes a reflection (other knots, such as the Figure-8 knot ## University of Oxford## Mathematical Institute News## Whitehead PrizeA Whitehead prize is awarded to Marc Lackenby of St. Catherine’s College and the University of Oxford for his contributions to three dimensional topology and to combinatorial group theory. He has proved two unexpected results about Dehn surgery, which is a much used method to construct a three-dimensional manifold M With Daryl Cooper he also proved a remarkable finiteness result that for a given M He has found other remarkable results about hyperbolic three dimensional manifolds. One is a simple algorithm enhancing Thurston’s famous result giving the existence of hyperbolic structures on a large class of three dimensional manifolds. The algorithm allows one to calculate (up to explicit bounds) the volume of the (hyperbolic) complement of a class of knots. Another of his theorems is related to the famous 2p theorem of Gromov and Thurston that a Dehn filling of a cusped hyperbolic manifold M His recent work on the Heegaard genus of coverings has opened up new relations with other areas of mathematics. By using comparatively elementary methods, he has found novel connections between the isoperimetric value of a Cayley graph of a finite group and the Betti numbers of a 2-complex associated with the presentation of the group. There are exciting possible consequences of this work in combinatorial group theory. |

Illiteracy and Topology-Adam and Eve: Topology don’t care about quantity but only works on quality. This reason makes it easy to work on unconsciousness and language which work the same way.

If you consider Illiteracy through Topology, the results are perfectly coherent and performing. Using only Quality references, makes you discover at once what is the problem : Sexuation !

What is Topology ? :Topology is a part of mathematics. Their is two separate, distinct sections (one on general, point set topology, the other on algebraic topology). Independent topics and applications exist too, like in psychoanalysis and in linguistics…

What is Psychoanalysis ? :Psychoanalysis is the name of a procedure for the investigation of mental processes which are almost inaccessible in any other way and can be the object of serious investigation. Psychoanalysis is concerned not only with the singular experience of an individual analysis, but is equally preoccupied with and applied to the entirety of human phenomena in which the unconscious is involved…