L9a55

From Knot Atlas
Jump to navigationJump to search

L9a54.gif

L9a54

L9n1.gif

L9n1

L9a55.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9a55 at Knotilus!

L9a55 is in the Rolfsen table of links.


Link Presentations

[edit Notes on L9a55's Link Presentations]

Planar diagram presentation X6172 X2536 X16,12,17,11 X10,3,11,4 X4,9,1,10 X14,7,15,8 X8,13,5,14 X18,16,13,15 X12,18,9,17
Gauss code {1, -2, 4, -5}, {2, -1, 6, -7}, {5, -4, 3, -9}, {7, -6, 8, -3, 9, -8}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gif
BraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart2.gif
BraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
A Morse Link Presentation L9a55 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in , , , ...) (db)
Jones polynomial (db)
Signature -1 (db)
HOMFLY-PT polynomial 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 a^7 z^{-1} +a^7 z^{-3} -3 z a^5-5 a^5 z^{-1} -3 a^5 z^{-3} +3 z^3 a^3+6 z a^3+7 a^3 z^{-1} +3 a^3 z^{-3} -z^5 a-2 z^3 a-3 z a-3 a z^{-1} -a z^{-3} +z^3 a^{-1} } (db)
Kauffman polynomial 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 -a^4 z^8-a^2 z^8-a^5 z^7-5 a^3 z^7-4 a z^7-a^6 z^6-a^4 z^6-6 a^2 z^6-6 z^6-a^7 z^5-3 a^5 z^5+4 a^3 z^5+2 a z^5-4 z^5 a^{-1} -2 a^4 z^4+7 a^2 z^4-z^4 a^{-2} +8 z^4+4 a^7 z^3+12 a^5 z^3+8 a^3 z^3+4 a z^3+4 z^3 a^{-1} +6 a^6 z^2+12 a^4 z^2+6 a^2 z^2-6 a^7 z-14 a^5 z-14 a^3 z-6 a z-8 a^6-15 a^4-8 a^2+4 a^7 z^{-1} +9 a^5 z^{-1} +9 a^3 z^{-1} +4 a z^{-1} +3 a^6 z^{-2} +6 a^4 z^{-2} +3 a^2 z^{-2} -a^7 z^{-3} -3 a^5 z^{-3} -3 a^3 z^{-3} -a z^{-3} } (db)

Khovanov Homology

The coefficients of the monomials 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 t^rq^j} are shown, along with their alternating sums 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 \chi} (fixed 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 j} , alternation over ).   
\ r
  \  
j \
-6-5-4-3-2-10123χ
6         1-1
4        3 3
2       31 -2
0      53  2
-2     67   1
-4    41    3
-6   16     5
-8  44      0
-10 15       4
-12          0
-141         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 Link Page master template (intermediate).

See/edit the Link_Splice_Base (expert).

Back to the top.

L9a54.gif

L9a54

L9n1.gif

L9n1