# K11a95

## Contents

 (Knotscape image) See the full Hoste-Thistlethwaite Table of 11 Crossing Knots. Visit K11a95's page at Knotilus! Visit K11a95's page at the original Knot Atlas!

### Knot presentations

 Planar diagram presentation X4251 X10,4,11,3 X12,6,13,5 X18,8,19,7 X2,10,3,9 X8,12,9,11 X22,14,1,13 X20,16,21,15 X6,18,7,17 X16,20,17,19 X14,22,15,21 Gauss code 1, -5, 2, -1, 3, -9, 4, -6, 5, -2, 6, -3, 7, -11, 8, -10, 9, -4, 10, -8, 11, -7 Dowker-Thistlethwaite code 4 10 12 18 2 8 22 20 6 16 14
A Braid Representative

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 2 Bridge index 2 Super bridge index Missing Nakanishi index Missing Maximal Thurston-Bennequin number Data:K11a95/ThurstonBennequinNumber Hyperbolic Volume 11.7607 A-Polynomial See Data:K11a95/A-polynomial

### Four dimensional invariants

 Smooth 4 genus Missing Topological 4 genus Missing Concordance genus 2 Rasmussen s-Invariant -4

### Polynomial invariants

 Alexander polynomial 6t2−18t + 25−18t−1 + 6t−2 Conway polynomial 6z4 + 6z2 + 1 2nd Alexander ideal (db, data sources) {1} Determinant and Signature { 73, 4 } Jones polynomial −q13 + 3q12−5q11 + 7q10−10q9 + 11q8−11q7 + 10q6−7q5 + 5q4−2q3 + q2 HOMFLY-PT polynomial (db, data sources) z4a−4 + 2z4a−6 + 2z4a−8 + z4a−10 + 2z2a−4 + 3z2a−6 + 2z2a−8−z2a−12 + a−4 + a−6−a−10 Kauffman polynomial (db, data sources) z10a−10 + z10a−12 + 2z9a−9 + 5z9a−11 + 3z9a−13 + 3z8a−8 + 2z8a−10 + 2z8a−12 + 3z8a−14 + 3z7a−7−15z7a−11−11z7a−13 + z7a−15 + 3z6a−6−3z6a−8−10z6a−10−17z6a−12−13z6a−14 + 2z5a−5−z5a−7−6z5a−9 + 10z5a−11 + 9z5a−13−4z5a−15 + z4a−4−3z4a−6 + 2z4a−8 + 9z4a−10 + 18z4a−12 + 15z4a−14−2z3a−5−2z3a−7 + 5z3a−9 + z3a−11 + 4z3a−15−2z2a−4 + 2z2a−6−z2a−8−5z2a−10−4z2a−12−4z2a−14 + 2za−7−za−9−3za−11−za−13−za−15 + a−4−a−6 + a−10 The A2 invariant Data:K11a95/QuantumInvariant/A2/1,0 The G2 invariant Data:K11a95/QuantumInvariant/G2/1,0

### "Similar" Knots (within the Atlas)

Same Alexander/Conway Polynomial: {10_53,}

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

### Vassiliev invariants

 V2 and V3: (6, 15)
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 24 120 288 732 92 2880 5008 800 568 2304 7200 17568 2208 $\frac{176751}{5}$ $\frac{25828}{15}$ $\frac{176164}{15}$ $\frac{929}{3}$ $\frac{6991}{5}$

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 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 = 4 is the signature of K11a95. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.
 \ r \ j \
01234567891011χ
27           1-1
25          2 2
23         31 -2
21        42  2
19       63   -3
17      54    1
15     66     0
13    45      -1
11   36       3
9  24        -2
7  3         3
512          -1
31           1
Integral Khovanov Homology
 $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ i = 3 i = 5 r = 0 ${\mathbb Z}$ ${\mathbb Z}$ r = 1 ${\mathbb Z}^{2}$ r = 2 ${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ r = 3 ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ r = 4 ${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ r = 5 ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{6}$ r = 6 ${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ r = 7 ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{6}$ r = 8 ${\mathbb Z}^{3}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ r = 9 ${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{3}$ ${\mathbb Z}^{3}$ r = 10 ${\mathbb Z}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ r = 11 ${\mathbb Z}_2$ ${\mathbb Z}$

### Computer Talk

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

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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