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Download KNOTORIOUS (32 bit version)
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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.

Knot u_a Alexander
polynomial 		Nak.
index 		det. sign max LT.
3_1
1

detected by
an unknotting move
1-t+t^2
Seifert matrix of 3_1
-1 0
-1 -1
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
1
3
First homology
of the double branched cover of 3_1
Z/3
-2 2
4_1
1

detected by
an unknotting move
-1+3t-t^2
Seifert matrix of 4_1
1 0
-1 -1
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
1
5
First homology
of the double branched cover of 4_1
Z/5
0 0
5_1
2

detected by
the signature
1-t+t^2-t^3+t^4
Seifert matrix of 5_1
-1 -1 0 -1
0 -1 0 0
-1 -1 -1 -1
0 -1 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
t^-1-1+t
5
First homology
of the double branched cover of 5_1
Z/5
-4 4
5_2
1

detected by
an unknotting move
2-3t+2t^2
Seifert matrix of 5_2
-1 -1
0 -2
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
1
7
First homology
of the double branched cover of 5_2
Z/7
-2 2
6_1
1

detected by
an unknotting move
-2+5t-2t^2
Seifert matrix of 6_1
1 0
1 -2
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
t^-1-2+t
9
First homology
of the double branched cover of 6_1
Z/9
0 0
6_2
1

detected by
an unknotting move
-1+3t-3t^2+3t^3-t^4
Seifert matrix of 6_2
1 0 0 0
-1 -1 -1 -1
-1 0 -1 0
-1 0 -1 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-t^-1+3-t
11
First homology
of the double branched cover of 6_2
Z/11
-2 2
6_3
1

detected by
an unknotting move
1-3t+5t^2-3t^3+t^4
Seifert matrix of 6_3
-1 0 0 0
-1 -1 0 0
-1 -1 1 1
0 0 0 1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-1
13
First homology
of the double branched cover of 6_3
Z/13
0 0
7_1
3

detected by
the signature
1-t+t^2-t^3+t^4-t^5+t^6
Seifert matrix of 7_1
-1 -1 -1 0 -1 -1
0 -1 -1 0 0 -1
0 0 -1 0 0 0
-1 -1 -1 -1 -1 -1
0 -1 -1 0 -1 -1
0 0 -1 0 0 -1
1
Generator of the Alexander module
(0,0,0,1,0,0)
the Blanchfield form on it
t^-2-t^-1+1-t+t^2
7
First homology
of the double branched cover of 7_1
Z/7
-6 6
7_2
1

detected by
an unknotting move
3-5t+3t^2
Seifert matrix of 7_2
-1 1
0 -3
1
Generator of the Alexander module
(1,0)
the Blanchfield form on it
1
11
First homology
of the double branched cover of 7_2
Z/11
-2 2
7_3
2

detected by
the signature
2-3t+3t^2-3t^3+2t^4
Seifert matrix of 7_3
-1 -1 -1 -1
0 -1 0 -1
0 -1 -1 -1
0 0 0 -2
1
Generator of the Alexander module
(2t^3,0,t^3,1)
the Blanchfield form on it
-5t^-2+18t^-1-24+18t-5t^2
13
First homology
of the double branched cover of 7_3
Z/13
-4 4
7_4
2

detected by
the Lickorish test
4-7t+4t^2
Seifert matrix of 7_4
-2 0
-1 -2
1
Generator of the Alexander module
(0,1)
the Blanchfield form on it
-2t^-1+4-2t
15
First homology
of the double branched cover of 7_4
Z/15
-2 2
7_5
2

detected by
the signature
2-4t+5t^2-4t^3+2t^4
Seifert matrix of 7_5
-1 0 -1 0
0 -1 -1 0
0 0 -2 0
0 -1 -1 -1
1
Generator of the Alexander module
(-t,0,1,1)
the Blanchfield form on it
2t^-1-2+2t
17
First homology
of the double branched cover of 7_5
Z/17
-4 4
7_6
1

detected by
an unknotting move
-1+5t-7t^2+5t^3-t^4
Seifert matrix of 7_6
-1 0 0 0
-1 -1 0 0
-1 -1 1 -1
0 0 0 -1
1
Generator of the Alexander module
(0,0,1,0)
the Blanchfield form on it
-2t^-1+3-2t
19
First homology
of the double branched cover of 7_6
Z/19
-2 2
7_7
1

detected by
an unknotting move
1-5t+9t^2-5t^3+t^4
Seifert matrix of 7_7
1 0 0 0
-1 -1 0 -1
0 0 1 0
-1 0 -1 -1
1
Generator of the Alexander module
(0,0,-1,1)
the Blanchfield form on it
t^-1-3+t
21
First homology
of the double branched cover of 7_7
Z/21
0 0