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(Knotscape image)
See the full Hoste-Thistlethwaite Table of 11 Crossing Knots.

Visit K11n95 at Knotilus!

Knot presentations

Planar diagram presentation X4251 X10,4,11,3 X14,6,15,5 X7,13,8,12 X2,10,3,9 X11,21,12,20 X18,14,19,13 X15,22,16,1 X6,18,7,17 X19,9,20,8 X21,16,22,17
Gauss code 1, -5, 2, -1, 3, -9, -4, 10, 5, -2, -6, 4, 7, -3, -8, 11, 9, -7, -10, 6, -11, 8
Dowker-Thistlethwaite code 4 10 14 -12 2 -20 18 -22 6 -8 -16
A Braid Representative
A Morse Link Presentation K11n95 ML.gif

Three dimensional invariants

Symmetry type Reversible
Unknotting number 2
3-genus 3
Bridge index 3
Super bridge index Missing
Nakanishi index Missing
Maximal Thurston-Bennequin number Data:K11n95/ThurstonBennequinNumber
Hyperbolic Volume 11.1971
A-Polynomial See Data:K11n95/A-polynomial

[edit Notes for K11n95's three dimensional invariants]

Four dimensional invariants

Smooth 4 genus Missing
Topological 4 genus Missing
Concordance genus 3
Rasmussen s-Invariant -4

[edit Notes for K11n95's four dimensional invariants]

Polynomial invariants

Alexander polynomial -t^3+5 t^2-7 t+7-7 t^{-1} +5 t^{-2} - t^{-3}
Conway polynomial -z^6-z^4+4 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 33, 4 }
Jones polynomial -2 q^9+4 q^8-5 q^7+6 q^6-6 q^5+5 q^4-3 q^3+2 q^2
HOMFLY-PT polynomial (db, data sources) -z^6 a^{-6} +2 z^4 a^{-4} -4 z^4 a^{-6} +z^4 a^{-8} +6 z^2 a^{-4} -5 z^2 a^{-6} +3 z^2 a^{-8} +3 a^{-4} -3 a^{-6} +2 a^{-8} - a^{-10}
Kauffman polynomial (db, data sources) z^8 a^{-6} +z^8 a^{-8} +z^7 a^{-5} +3 z^7 a^{-7} +2 z^7 a^{-9} -2 z^6 a^{-6} -z^6 a^{-8} +z^6 a^{-10} -z^5 a^{-5} -5 z^5 a^{-7} -4 z^5 a^{-9} +3 z^4 a^{-4} +6 z^4 a^{-6} +5 z^4 a^{-8} +2 z^4 a^{-10} +4 z^3 a^{-7} +7 z^3 a^{-9} +3 z^3 a^{-11} -7 z^2 a^{-4} -9 z^2 a^{-6} -6 z^2 a^{-8} -4 z^2 a^{-10} -z a^{-5} -z a^{-7} -3 z a^{-9} -3 z a^{-11} +3 a^{-4} +3 a^{-6} +2 a^{-8} + a^{-10}
The A2 invariant Data:K11n95/QuantumInvariant/A2/1,0
The G2 invariant Data:K11n95/QuantumInvariant/G2/1,0

"Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {9_11,}

Same Jones Polynomial (up to mirroring, q\leftrightarrow q^{-1}): {}

Vassiliev invariants

V2 and V3: (4, 9)
V2,1 through V6,9:
V2,1 V3,1 V4,1 V4,2 V4,3 V5,1 V5,2 V5,3 V5,4 V6,1 V6,2 V6,3 V6,4 V6,5 V6,6 V6,7 V6,8 V6,9
16 72 128 \frac{1208}{3} \frac{208}{3} 1152 2416 448 360 \frac{2048}{3} 2592 \frac{19328}{3} \frac{3328}{3} \frac{219182}{15} \frac{384}{5} \frac{285008}{45} \frac{1090}{9} \frac{12782}{15}

V2,1 through V6,9 were provided by Petr Dunin-Barkowski <barkovs@itep.ru>, Andrey Smirnov <asmirnov@itep.ru>, and Alexei Sleptsov <sleptsov@itep.ru> and uploaded on October 2010 by User:Drorbn. Note that they are normalized differently than V2 and V3.

Khovanov Homology

The coefficients of the monomials t^rq^j are shown, along with their alternating sums \chi (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=4 is the signature of K11n95. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.   
\ r
j \
19       2-2
17      2 2
15     32 -1
13    32  1
11   33   0
9  23    -1
7 13     2
512      -1
32       2
Integral Khovanov Homology

(db, data source)

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

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 Hoste-Thistlethwaite Knot Page master template (intermediate).

See/edit the Hoste-Thistlethwaite_Splice_Base (expert).

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