# K11a93

## Contents

 (Knotscape image) See the full Hoste-Thistlethwaite Table of 11 Crossing Knots. Visit K11a93's page at Knotilus! Visit K11a93's page at the original Knot Atlas!

### Knot presentations

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

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 2 Super bridge index Missing Nakanishi index Missing Maximal Thurston-Bennequin number Data:K11a93/ThurstonBennequinNumber Hyperbolic Volume 13.1112 A-Polynomial See Data:K11a93/A-polynomial

### Four dimensional invariants

 Smooth 4 genus Missing Topological 4 genus Missing Concordance genus 3 Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial −2t3 + 10t2−21t + 27−21t−1 + 10t−2−2t−3 Conway polynomial −2z6−2z4 + z2 + 1 2nd Alexander ideal (db, data sources) {1} Determinant and Signature { 93, 0 } Jones polynomial q4−3q3 + 6q2−10q + 13−14q−1 + 15q−2−12q−3 + 9q−4−6q−5 + 3q−6−q−7 HOMFLY-PT polynomial (db, data sources) −z2a6−a6 + 2z4a4 + 4z2a4 + a4−z6a2−2z4a2 + 2a2−z6−3z4−4z2−2 + z4a−2 + 2z2a−2 + a−2 Kauffman polynomial (db, data sources) a4z10 + a2z10 + 3a5z9 + 6a3z9 + 3az9 + 3a6z8 + 5a4z8 + 7a2z8 + 5z8 + a7z7−8a5z7−12a3z7 + 3az7 + 6z7a−1−12a6z6−25a4z6−20a2z6 + 5z6a−2−2z6−4a7z5−2a3z5−15az5−6z5a−1 + 3z5a−3 + 14a6z4 + 26a4z4 + 11a2z4−5z4a−2 + z4a−4−7z4 + 5a7z3 + 9a5z3 + 8a3z3 + 9az3 + 2z3a−1−3z3a−3−5a6z2−9a4z2−a2z2 + 3z2a−2−z2a−4 + 7z2−2a7z−3a5z−2a3z−az + za−1 + za−3 + a6 + a4−2a2−a−2−2 The A2 invariant Data:K11a93/QuantumInvariant/A2/1,0 The G2 invariant Data:K11a93/QuantumInvariant/G2/1,0

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

Same Alexander/Conway Polynomial: {10_114,}

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

### Vassiliev invariants

 V2 and V3: (1, -3)
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 4 −24 8 $\frac{206}{3}$ $\frac{58}{3}$ −96 −208 0 −56 $\frac{32}{3}$ 288 $\frac{824}{3}$ $\frac{232}{3}$ $\frac{28831}{30}$ $-\frac{34}{5}$ $\frac{17942}{45}$ $\frac{641}{18}$ $\frac{991}{30}$

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 = 0 is the signature of K11a93. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.
 \ r \ j \
-7-6-5-4-3-2-101234χ
9           11
7          2 -2
5         41 3
3        62  -4
1       74   3
-1      87    -1
-3     76     1
-5    58      3
-7   47       -3
-9  25        3
-11 14         -3
-13 2          2
-151           -1
Integral Khovanov Homology
 $\dim{\mathcal G}_{2r+i}\operatorname{KH}^r_{\mathbb Z}$ i = −1 i = 1 r = −7 ${\mathbb Z}$ r = −6 ${\mathbb Z}^{2}\oplus{\mathbb Z}_2$ ${\mathbb Z}$ r = −5 ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ r = −4 ${\mathbb Z}^{5}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ r = −3 ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{5}$ ${\mathbb Z}^{5}$ r = −2 ${\mathbb Z}^{8}\oplus{\mathbb Z}_2^{7}$ ${\mathbb Z}^{7}$ r = −1 ${\mathbb Z}^{6}\oplus{\mathbb Z}_2^{8}$ ${\mathbb Z}^{8}$ r = 0 ${\mathbb Z}^{7}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{7}$ r = 1 ${\mathbb Z}^{4}\oplus{\mathbb Z}_2^{6}$ ${\mathbb Z}^{6}$ r = 2 ${\mathbb Z}^{2}\oplus{\mathbb Z}_2^{4}$ ${\mathbb Z}^{4}$ r = 3 ${\mathbb Z}\oplus{\mathbb Z}_2^{2}$ ${\mathbb Z}^{2}$ 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.

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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