This is the simplest 3-page diagram of knot 3_1 (the trefoil knot).

This is the simplest non-trivial knot. Its simplest planar diagram has 3 crossings. A list of other knots with small crossing number can be found in [1] and [2]. 3_1 is an alternating knot. It is chiral and invertible. It is also the torus knot of type (2,3). Here we give the simplest 3-page diagram of the trefoil knot. It has 8 vertices. 3-page diagrams were introduced in [3]. According to the notation given in [3] this diagram is encoded by the word a_1a_0a_0d_2d_1c_0c_0c_2.

Keywords
| knot; link; 3-page representation | |

MSC-2000 Classification
| 57M25 | |

Zentralblatt No.
| 01682976 |

- D. Rolfsen: Knots and Links, Publish or Perish, Houston (1990).
- C. Cerf:
*Atlas of oriented knots and links*, http://at.yorku.ca/t/a/i/c/31.dir/cerf.htm. - I. Dynnikov:
*Three-page approach to knot theory. Encoding and local moves*, Functional Analysis and Its Appl.**33**, 4 (1999), 260--269. - I. Dynnikov:
*Three-page approach to knot theory. Universal semigroup*, Functional Analysis and Its Appl.**34**, 1 (2000), 24--32.

- Master File: TrefoilLeft_Master.jvx
- Applet File: TrefoilLeft_Applet.jvx
- Preview: TrefoilLeft_Preview.gif
- Other: TrefoilLeft_Other.jkb

Submitted: Sun Sep 10 07:10:24 CET 2000.

Accepted: Mon Nov 20 17:06:57 CET 2000.

Moscow State University

Department of Mechanics and Mathematics

Vorobyovy gory

Moscow 119899

Russia

dynnikov@mech.math.msu.su

http://mech.math.msu.su/~dynnikov