K11n8

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K11n7.gif

K11n7

K11n9.gif

K11n9

K11n8.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n8 at Knotilus!


Knot K11n8.
A graph, knot K11n8.
A part of a knot and a part of a graph.

Knot presentations

Planar diagram presentation X4251 X8394 X10,6,11,5 X7,14,8,15 X2,9,3,10 X11,18,12,19 X13,6,14,7 X15,20,16,21 X17,12,18,13 X19,22,20,1 X21,16,22,17
Gauss code 1, -5, 2, -1, 3, 7, -4, -2, 5, -3, -6, 9, -7, 4, -8, 11, -9, 6, -10, 8, -11, 10
Dowker-Thistlethwaite code 4 8 10 -14 2 -18 -6 -20 -12 -22 -16
A Braid Representative {{{braid_table}}}
A Morse Link Presentation K11n8 ML.gif

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 4

[edit Notes for K11n8's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 53, -4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n8/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n8/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {K11n59,}

Same Jones Polynomial (up to mirroring, ): {}

Vassiliev invariants

V2 and V3: (3, -6)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

Khovanov Homology

The coefficients of the monomials are shown, along with their alternating sums (fixed , alternation over ). The squares with yellow highlighting are those on the "critical diagonals", where or , where -4 is the signature of K11n8. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-7-6-5-4-3-2-1012χ
1         11
-1        2 -2
-3       41 3
-5      43  -1
-7     53   2
-9    44    0
-11   45     -1
-13  24      2
-15 14       -3
-17 2        2
-191         -1
Integral Khovanov Homology

(db, data source)

  

Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

Modifying This Page

Read me first: Modifying Knot Pages.

See/edit the Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

Back to the top.

K11n7.gif

K11n7

K11n9.gif

K11n9