K11n75

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K11n74.gif

K11n74

K11n76.gif

K11n76

K11n75.gif
(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n75 at Knotilus!



Knot presentations

Planar diagram presentation X4251 X8493 X5,14,6,15 X2837 X9,20,10,21 X11,16,12,17 X13,6,14,7 X15,18,16,19 X17,12,18,13 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 K11n75 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number
3-genus 3
Bridge index 4
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n75/ThurstonBennequinNumber
Hyperbolic Volume 13.5931
A-Polynomial See Data:K11n75/A-polynomial

[edit Notes for K11n75's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus
Rasmussen s-Invariant 2

[edit Notes for K11n75's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 63, -2 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant Data:K11n75/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n75/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_65, 10_77, K11n71,}

Same Jones Polynomial (up to mirroring, ): {K11n71,}

Vassiliev invariants

V2 and V3: (4, -5)
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 -2 is the signature of K11n75. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-8-7-6-5-4-3-2-101χ
1         2-2
-1        3 3
-3       53 -2
-5      62  4
-7     45   1
-9    66    0
-11   34     1
-13  26      -4
-15 13       2
-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.

K11n74.gif

K11n74

K11n76.gif

K11n76