L9a46

From Knot Atlas
Jump to: navigation, search

L9a45.gif

L9a45

L9a47.gif

L9a47

Contents

L9a46.gif
(Knotscape image)
See the full Thistlethwaite Link Table (up to 11 crossings).

Visit L9a46 at Knotilus!

L9a46 is 9^3_{10} in the Rolfsen table of links.


Link Presentations

[edit Notes on L9a46's Link Presentations]

Planar diagram presentation X6172 X12,6,13,5 X8493 X2,14,3,13 X14,7,15,8 X16,12,17,11 X18,9,11,10 X10,17,5,18 X4,15,1,16
Gauss code {1, -4, 3, -9}, {2, -1, 5, -3, 7, -8}, {6, -2, 4, -5, 9, -6, 8, -7}
A Braid Representative
BraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart4.gifBraidPart1.gifBraidPart0.gifBraidPart1.gif
BraidPart0.gifBraidPart2.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart2.gifBraidPart3.gifBraidPart2.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart4.gifBraidPart0.gif
A Morse Link Presentation L9a46 ML.gif

Polynomial invariants

Multivariable Alexander Polynomial (in u, v, w, ...) -\frac{(u-1) (v-1)^2 (w-1)^2}{\sqrt{u} v w} (db)
Jones polynomial - q^{-5} +q^4+4 q^{-4} -4 q^3-6 q^{-3} +7 q^2+10 q^{-2} -9 q-10 q^{-1} +12 (db)
Signature 0 (db)
HOMFLY-PT polynomial -a^4 z^2+a^4 z^{-2} +2 a^2 z^4+z^4 a^{-2} +3 a^2 z^2+z^2 a^{-2} -2 a^2 z^{-2} -a^2-z^6-3 z^4-3 z^2+ z^{-2} +1 (db)
Kauffman polynomial a^5 z^5-a^5 z^3+4 a^4 z^6-8 a^4 z^4+z^4 a^{-4} +4 a^4 z^2-a^4 z^{-2} +a^4+5 a^3 z^7-8 a^3 z^5+4 z^5 a^{-3} +2 a^3 z^3-3 z^3 a^{-3} -a^3 z+2 a^3 z^{-1} +2 a^2 z^8+8 a^2 z^6+7 z^6 a^{-2} -23 a^2 z^4-9 z^4 a^{-2} +12 a^2 z^2+4 z^2 a^{-2} -2 a^2 z^{-2} +a^2+11 a z^7+6 z^7 a^{-1} -17 a z^5-4 z^5 a^{-1} +4 a z^3-2 z^3 a^{-1} -a z+2 a z^{-1} +2 z^8+11 z^6-25 z^4+12 z^2- z^{-2} +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 \
-5-4-3-2-101234χ
9         11
7        3 -3
5       41 3
3      53  -2
1     74   3
-1    57    2
-3   55     0
-5  37      4
-7 13       -2
-9 3        3
-111         -1
Integral Khovanov Homology

(db, data source)

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

Back to the top.

L9a45.gif

L9a45

L9a47.gif

L9a47