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12 non-alternating
all knots up to 12 crossings maybe slow
discussion of unknown values
statistics of invariants
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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.

List of problematic knots
The following knots have algebraic unknotting number 1 or 2.
12a_0050 12a_0141 12a_0364 12a_0649 12a_0728 12a_0791 12a_0901
12a_1049 12a_1054 12a_1064 12a_1138 12a_1141 12a_1234 12a_1236
12a_1264 12n_0200 12n_0260 12n_0657 12n_0864



Presentation matrice for the Alexander modules of the 5 knots with unknown Nakanishi index
Knot Presentation matrix
12a_1054 2t^3 -1+4t-7t^2+4t^3-t^4
1-5t+t^2-5t^3+t^4 3t
12a_1141 1+2t 2-2t+t^2
4t-9t^2+6t^3-8t^4+6t^5-t^6 1-2t
12a_1264 2-5t 1-5t+4t^2-t^3
6-14t-6t^2-7t^3-2t^5 2-13t+3t^2
12n_0260 1-4t^2 4-4t-5t^3+t^4-t^5
-t+3t^2-t^3 -1+3t^2
12n_0657 11 59-27t+11t^2-3t^3
2+t 11


Blanchfield pairings for the 14 knots with Nakanishi index 1
Knot Alexander polynomial Blanchfield pairing of the generator
12a_0050 -8z_3+20z_2-30z_1+3 -z_3+7z_2-13z_1+17
12a_0141 -z_4+7z_3-20z_2+33z_1-39 z_2+4z_1-8
12a_0364 z_4-8z_3+29z_2-63z_1+81 -2z_2+10z_1-15
12a_0649 -z_4+7z_3-17z_2+25z_1-27 z_2-z_1+1
12a_0728 2z_4-8z_3+17z_2-25z_1+29 4z_2-9z_1+14
12a_0791 3z_3-9z_2+13z_1-13 z_2-z_1+1
12a_0901 -z_4+9z_3-27z_2+47z_1-55 -2z_3+7z_2-13z_1+15
12a_1064 -2z_4+9z_3-21z_2+33z_1-37 z_2-z_1+2
12a_1138 3z_3-11z_2+17z_1-17 3z_2-11z_1+17
12a_1234 -2z_4+7z_3-15z_2+25z_1-29 -2z_2+5z_1-6
12a_1236 -2z_4+9z_3-21z_2+33z_1-37 -z_2+z_1-2
12n_0200 2z_2-2z_1+1 2z_1-4
12n_0864 z_4-5z_3+15z_2-28z_1+33 -z_2+2z_1-5