L11a15

From Knot Atlas

Jump to: navigation, search

L11a14

L11a16

Contents

Image:L11a15.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L11a15's page at Knotilus.

Visit L11a15's page at the original Knot Atlas.


[edit] Link Presentations

[edit Notes on L11a15's Link Presentations]

Planar diagram presentation X6172 X12,7,13,8 X4,13,1,14 X18,10,19,9 X8493 X14,6,15,5 X22,16,5,15 X20,18,21,17 X16,22,17,21 X10,20,11,19 X2,12,3,11
Gauss code {1, -11, 5, -3}, {6, -1, 2, -5, 4, -10, 11, -2, 3, -6, 7, -9, 8, -4, 10, -8, 9, -7}
A Braid Representative
Image:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart4.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart3.gifImage:BraidPart4.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart3.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart1.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart4.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart0.gifImage:BraidPart1.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart1.gifImage:BraidPart2.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart0.gifImage:BraidPart1.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart3.gifImage:BraidPart2.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart1.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gifImage:BraidPart3.gif
Image:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart2.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart0.gifImage:BraidPart4.gif
A Morse Link Presentation Image:L11a15_ML.gif

[edit] Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) \frac{(u-1) (v-1) \left(3 v^2-5 v+3\right)}{\sqrt{u} v^{3/2}} (db)
Jones polynomial -12 q^{9/2}+13 q^{7/2}-14 q^{5/2}+\frac{1}{q^{5/2}}+11 q^{3/2}-\frac{3}{q^{3/2}}-q^{17/2}+4 q^{15/2}-6 q^{13/2}+9 q^{11/2}-9 \sqrt{q}+\frac{5}{\sqrt{q}} (db)
Signature 1 (db)
HOMFLY-PT polynomial z3a−7 + a−7z−1 + z5a−5 + z3a−5za−5−2a−5z−1 + z5a−3za−3 + z5a−1az3 + 2z3a−1az + 3za−1 + a−1z−1 (db)
Kauffman polynomial z7a−9−3z5a−9 + z3a−9 + 4z8a−8−16z6a−8 + 15z4a−8z2a−8−2a−8 + 5z9a−7−20z7a−7 + 21z5a−7−6z3a−7 + a−7z−1 + 2z10a−6−21z6a−6 + 24z4a−6 + z2a−6−5a−6 + 9z9a−5−33z7a−5 + 36z5a−5−13z3a−5za−5 + 2a−5z−1 + 2z10a−4−11z6a−4 + 9z4a−4 + 2z2a−4−3a−4 + 4z9a−3−8z7a−3 + 9z5a−3−9z3a−3 + 2za−3 + 4z8a−2−2z6a−2 + a2z4−4z4a−2a2z2 + z2a−2 + a−2 + 4z7a−1 + 3az5−4az3−7z3a−1 + 2az + 5za−1a−1z−1 + 4z6−3z4 (db)

[edit] Khovanov Homology

The coefficients of the monomials trqj are shown, along with their alternating sums χ (fixed j, alternation over r). The squares with yellow highlighting are those on the "critical diagonals", where j−2r = s + 1 or j−2r = s−1, where s = 1 is the signature of L11a15. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.    Data:L11a15/KhovanovTable
Integral Khovanov Homology

(db, data source)

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

[edit] Computer Talk

Much of the above data can be recomputed by Mathematica using the package KnotTheory`. See A Sample KnotTheory` Session.

[edit] 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.

L11a14

L11a16

Personal tools