9 7

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9 6.gif

9_6

9 8.gif

9_8

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9 7 Quick Notes


9 7 Further Notes and Views

Knot presentations

Planar diagram presentation X1425 X3,12,4,13 X5,16,6,17 X7,18,8,1 X17,6,18,7 X9,14,10,15 X13,10,14,11 X15,8,16,9 X11,2,12,3
Gauss code -1, 9, -2, 1, -3, 5, -4, 8, -6, 7, -9, 2, -7, 6, -8, 3, -5, 4
Dowker-Thistlethwaite code 4 12 16 18 14 2 10 8 6
Conway Notation [342]

Minimum Braid Representative:

BraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart4.gif

Length is 11, width is 4.

Braid index is 4.

A Morse Link Presentation:

9 7 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 2
Bridge index 2
Super bridge index
Nakanishi index 1
Maximal Thurston-Bennequin number [-14][3]
Hyperbolic Volume 8.01486
A-Polynomial See Data:9 7/A-polynomial

[edit Notes for 9 7's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 9 7's four dimensional invariants]

Polynomial invariants

Alexander polynomial
Conway polynomial
2nd Alexander ideal (db, data sources)
Determinant and Signature { 29, -4 }
Jones polynomial
HOMFLY-PT polynomial (db, data sources)
Kauffman polynomial (db, data sources)
The A2 invariant
The G2 invariant

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {...}

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

Vassiliev invariants

V2 and V3: (5, -12)
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 9 7. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
  \  
j \
-9-8-7-6-5-4-3-2-10χ
-3         11
-5        110
-7       2  2
-9      21  -1
-11     32   1
-13    22    0
-15   23     -1
-17  12      1
-19 12       -1
-21 1        1
-231         -1
Integral Khovanov Homology

(db, data source)

  

The Coloured Jones Polynomials