K11n74

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K11n73.gif

K11n73

K11n75.gif

K11n75

K11n74.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n74 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8493 X5,14,6,15 X2837 X9,20,10,21 X16,12,17,11 X13,6,14,7 X18,16,19,15 X12,18,13,17 X19,22,20,1 X21,10,22,11
Gauss code 1, -4, 2, -1, -3, 7, 4, -2, -5, 11, 6, -9, -7, 3, 8, -6, 9, -8, -10, 5, -11, 10
Dowker-Thistlethwaite code 4 8 -14 2 -20 16 -6 18 12 -22 -10
A Braid Representative
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A Morse Link Presentation K11n74 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 2
Bridge index 4
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n74/ThurstonBennequinNumber
Hyperbolic Volume 10.4045
A-Polynomial See Data:K11n74/A-polynomial

[edit Notes for K11n74's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 0

[edit Notes for K11n74's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 9, 0 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n74/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n74/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {8_20, 10_140, K11n73,}

Same Jones Polynomial (up to mirroring, ): {K11n73,}

Vassiliev invariants

V2 and V3: (2, -2)
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
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{6391}{15}}

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 0 is the signature of K11n74. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-5-4-3-2-10123456χ
13           11
11          1 -1
9         11 0
7        21  -1
5      111   -1
3      12    1
1    131     1
-1   1 2      3
-3   11       0
-5 11         0
-7            0
-91           -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).

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K11n73.gif

K11n73

K11n75.gif

K11n75