L11a392

From Knot Atlas
Jump to: navigation, search

L11a391.gif

L11a391

L11a393.gif

L11a393

Contents

L11a392.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a392 at Knotilus!


Link Presentations

[edit Notes on L11a392's Link Presentations]

Planar diagram presentation X6172 X10,3,11,4 X16,7,17,8 X8,15,5,16 X18,11,19,12 X22,17,9,18 X12,21,13,22 X20,13,21,14 X14,19,15,20 X2536 X4,9,1,10
Gauss code {1, -10, 2, -11}, {10, -1, 3, -4}, {11, -2, 5, -7, 8, -9, 4, -3, 6, -5, 9, -8, 7, -6}
A Braid Representative
BraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart2.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart1.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart4.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gif
A Morse Link Presentation L11a392 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{2 t(1) t(3)^3+2 t(2) t(3)^3-2 t(3)^3-7 t(1) t(3)^2+4 t(1) t(2) t(3)^2-7 t(2) t(3)^2+5 t(3)^2+7 t(1) t(3)-5 t(1) t(2) t(3)+7 t(2) t(3)-4 t(3)-2 t(1)+2 t(1) t(2)-2 t(2)}{\sqrt{t(1)} \sqrt{t(2)} t(3)^{3/2}} (db)
Jones polynomial  q^{-2} -4 q^{-3} +10 q^{-4} -13 q^{-5} +18 q^{-6} -18 q^{-7} +19 q^{-8} -14 q^{-9} +10 q^{-10} -6 q^{-11} +2 q^{-12} - q^{-13} (db)
Signature -4 (db)
HOMFLY-PT polynomial -a^{14} z^{-2} +3 a^{12} z^{-2} +4 a^{12}-6 z^2 a^{10}-2 a^{10} z^{-2} -7 a^{10}+3 z^4 a^8+2 z^2 a^8-a^8 z^{-2} -a^8+4 z^4 a^6+7 z^2 a^6+a^6 z^{-2} +4 a^6+z^4 a^4 (db)
Kauffman polynomial z^7 a^{15}-5 z^5 a^{15}+9 z^3 a^{15}-7 z a^{15}+2 a^{15} z^{-1} +2 z^8 a^{14}-7 z^6 a^{14}+7 z^4 a^{14}-2 z^2 a^{14}-a^{14} z^{-2} +a^{14}+2 z^9 a^{13}-z^7 a^{13}-17 z^5 a^{13}+35 z^3 a^{13}-27 z a^{13}+8 a^{13} z^{-1} +z^{10} a^{12}+6 z^8 a^{12}-25 z^6 a^{12}+24 z^4 a^{12}-7 z^2 a^{12}-3 a^{12} z^{-2} +5 a^{12}+7 z^9 a^{11}-7 z^7 a^{11}-27 z^5 a^{11}+50 z^3 a^{11}-34 z a^{11}+10 a^{11} z^{-1} +z^{10} a^{10}+15 z^8 a^{10}-40 z^6 a^{10}+27 z^4 a^{10}-8 z^2 a^{10}-2 a^{10} z^{-2} +4 a^{10}+5 z^9 a^9+8 z^7 a^9-35 z^5 a^9+26 z^3 a^9-10 z a^9+2 a^9 z^{-1} +11 z^8 a^8-12 z^6 a^8-2 z^4 a^8+4 z^2 a^8+a^8 z^{-2} -3 a^8+13 z^7 a^7-16 z^5 a^7+2 z^3 a^7+4 z a^7-2 a^7 z^{-1} +10 z^6 a^6-11 z^4 a^6+7 z^2 a^6+a^6 z^{-2} -4 a^6+4 z^5 a^5+z^4 a^4 (db)

Khovanov Homology

The coefficients of the monomials t^rq^j are shown, along with their alternating sums \chi (fixed j, alternation over r).   
\ r
  \  
j \
-11-10-9-8-7-6-5-4-3-2-10χ
-3           11
-5          41-3
-7         6  6
-9        74  -3
-11       116   5
-13      1010    0
-15     98     1
-17    510      5
-19   59       -4
-21  15        4
-23 15         -4
-25 1          1
-271           -1
Integral Khovanov Homology

(db, data source)

  
\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z} i=-5 i=-3
r=-11 {\mathbb Z}
r=-10 {\mathbb Z}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-9 {\mathbb Z}^{5}\oplus{\mathbb Z}_2 {\mathbb Z}
r=-8 {\mathbb Z}^{5}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-7 {\mathbb Z}^{9}\oplus{\mathbb Z}_2^{5} {\mathbb Z}^{5}
r=-6 {\mathbb Z}^{10}\oplus{\mathbb Z}_2^{9} {\mathbb Z}^{9}
r=-5 {\mathbb Z}^{8}\oplus{\mathbb Z}_2^{10} {\mathbb Z}^{10}
r=-4 {\mathbb Z}^{10}\oplus{\mathbb Z}_2^{8} {\mathbb Z}^{11}
r=-3 {\mathbb Z}^{6}\oplus{\mathbb Z}_2^{7} {\mathbb Z}^{7}
r=-2 {\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6} {\mathbb Z}^{6}
r=-1 {\mathbb Z}_2^{4} {\mathbb Z}^{4}
r=0 {\mathbb Z} {\mathbb Z}

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.

L11a391.gif

L11a391

L11a393.gif

L11a393