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

Visit L9a29 at Knotilus!

L9a29 is 9^2_{19} in the Rolfsen table of links.

Link Presentations

[edit Notes on L9a29's Link Presentations]

Planar diagram presentation X8192 X2,9,3,10 X10,3,11,4 X6718 X16,11,17,12 X14,6,15,5 X4,16,5,15 X18,13,7,14 X12,17,13,18
Gauss code {1, -2, 3, -7, 6, -4}, {4, -1, 2, -3, 5, -9, 8, -6, 7, -5, 9, -8}
A Braid Representative
A Morse Link Presentation L9a29 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{u^2 v^4-u^2 v^3+u^2 v^2-u^2 v-u v^4+u v^3-u v^2+u v-u-v^3+v^2-v+1}{u v^2} (db)
Jones polynomial -\frac{1}{\sqrt{q}}+\frac{1}{q^{3/2}}-\frac{3}{q^{5/2}}+\frac{3}{q^{7/2}}-\frac{4}{q^{9/2}}+\frac{4}{q^{11/2}}-\frac{4}{q^{13/2}}+\frac{3}{q^{15/2}}-\frac{2}{q^{17/2}}+\frac{1}{q^{19/2}} (db)
Signature -5 (db)
HOMFLY-PT polynomial a^7 \left(-z^5\right)-4 a^7 z^3-4 a^7 z-a^7 z^{-1} +a^5 z^7+6 a^5 z^5+12 a^5 z^3+10 a^5 z+3 a^5 z^{-1} -a^3 z^5-5 a^3 z^3-7 a^3 z-2 a^3 z^{-1} (db)
Kauffman polynomial a^{12} z^2+2 a^{11} z^3+3 a^{10} z^4-2 a^{10} z^2+4 a^9 z^5-7 a^9 z^3+2 a^9 z+4 a^8 z^6-10 a^8 z^4+5 a^8 z^2-a^8+3 a^7 z^7-9 a^7 z^5+6 a^7 z^3-3 a^7 z+a^7 z^{-1} +a^6 z^8-11 a^6 z^4+13 a^6 z^2-3 a^6+4 a^5 z^7-19 a^5 z^5+27 a^5 z^3-14 a^5 z+3 a^5 z^{-1} +a^4 z^8-4 a^4 z^6+2 a^4 z^4+5 a^4 z^2-3 a^4+a^3 z^7-6 a^3 z^5+12 a^3 z^3-9 a^3 z+2 a^3 z^{-1} (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 \
0         11
-2          0
-4       31 2
-6      11  0
-8     32   1
-10    22    0
-12   22     0
-14  12      1
-16 12       -1
-18 1        1
-201         -1
Integral Khovanov Homology

(db, data source)

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

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