Shorthands denote
u_a algebraic unknotting number
Nak Nakanishi index
det determinant
sign signature
max LT maximum absolute value of
Levine-Tristram signatures
Hidden features
Click on to see
algebraic unknotting number how it has been detected
Alexander polynomial a Seifert matrix
(nondegenerate representative in the S-equivalence class)
Nakanishi index generator of the Alexander module,
if Nakanishi index is 1
Determinant H_1 of the double branched cover

 Welcome to the KNOTORIOUS world wide web page! set up by Maciej Borodzik mcboro'at'mimuw;edu;pl and Stefan Friedl sfriedl'at'gmail;com last update of the webpage 19 Feb 2012 last update of the knotorious data 01 Dec 2011
You may freely contact the authors in case of any questions.

• Click on the menu in the top left corner of the page to choose the knots, which you want to see.
• In the table of unknotting numbers, a green entry can be clicked on and reveals some hidden data. It is explained in the table on the left. Click once again, to hide the entry.
• A red entry has a different meaning. It shows, what criterion was used to give the lower bound for the algebraic unknotting number. For example, if a knot has unknotting number 3, and to prove this we used the fact that its signature is -6, then the entry for the signature will be highlighted. Please remark, that sometimes this is not the single criterion, which detects the unknotting number.
• On clicking on the Nakanishi index entry, if n(K)=1, then the generator of the Alexander module is given. It should be understood as follows. We consider a Seifert matrix V of size n, and a module Z[t,t^{-1}]^n. The generator is regarded as an element in this module. Its image under the quotient map (dividing by Vt-V^T) generates the Alexander module.
• Wherever we give a Seifert matrix, it is actually a matrix S-equivalent to a geometric Seifert matrix of a given knot. In particular, all Seifert matrices we give are non-degenerate.