# 9 34 (KnotPlot image) See the full Rolfsen Knot Table. Visit 9 34's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 34 at Knotilus!

### Knot presentations

 Planar diagram presentation X6271 X16,8,17,7 X8394 X2,15,3,16 X14,9,15,10 X10,6,11,5 X4,14,5,13 X18,11,1,12 X12,17,13,18 Gauss code 1, -4, 3, -7, 6, -1, 2, -3, 5, -6, 8, -9, 7, -5, 4, -2, 9, -8 Dowker-Thistlethwaite code 6 8 10 16 14 18 4 2 12 Conway Notation [8*20]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 1 3-genus 3 Bridge index 3 Super bridge index $\{4,6\}$ Nakanishi index 1 Maximal Thurston-Bennequin number [-6][-5] Hyperbolic Volume 14.3446 A-Polynomial See Data:9 34/A-polynomial

### Four dimensional invariants

 Smooth 4 genus $1$ Topological 4 genus $1$ Concordance genus $3$ Rasmussen s-Invariant 0

### Polynomial invariants

 Alexander polynomial $-t^3+6 t^2-16 t+23-16 t^{-1} +6 t^{-2} - t^{-3}$ Conway polynomial $-z^6-z^2+1$ 2nd Alexander ideal (db, data sources) $\{1\}$ Determinant and Signature { 69, 0 } Jones polynomial $q^4-4 q^3+8 q^2-10 q+12-12 q^{-1} +10 q^{-2} -7 q^{-3} +4 q^{-4} - q^{-5}$ HOMFLY-PT polynomial (db, data sources) $-z^6+2 a^2 z^4+z^4 a^{-2} -3 z^4-a^4 z^2+3 a^2 z^2+z^2 a^{-2} -4 z^2+a^2+ a^{-2} -1$ Kauffman polynomial (db, data sources) $3 a^2 z^8+3 z^8+6 a^3 z^7+14 a z^7+8 z^7 a^{-1} +4 a^4 z^6+5 a^2 z^6+8 z^6 a^{-2} +9 z^6+a^5 z^5-11 a^3 z^5-26 a z^5-10 z^5 a^{-1} +4 z^5 a^{-3} -7 a^4 z^4-19 a^2 z^4-10 z^4 a^{-2} +z^4 a^{-4} -23 z^4-a^5 z^3+5 a^3 z^3+12 a z^3+4 z^3 a^{-1} -2 z^3 a^{-3} +3 a^4 z^2+10 a^2 z^2+4 z^2 a^{-2} +11 z^2-a z-z a^{-1} -a^2- a^{-2} -1$ The A2 invariant $-q^{16}+q^{14}+2 q^{12}-2 q^{10}+2 q^8-q^6-q^4+2 q^2-2+3 q^{-2} -2 q^{-4} + q^{-6} +2 q^{-8} -2 q^{-10} + q^{-12}$ The G2 invariant $q^{80}-3 q^{78}+7 q^{76}-13 q^{74}+14 q^{72}-12 q^{70}-q^{68}+27 q^{66}-55 q^{64}+83 q^{62}-84 q^{60}+44 q^{58}+24 q^{56}-112 q^{54}+181 q^{52}-188 q^{50}+127 q^{48}-11 q^{46}-114 q^{44}+205 q^{42}-213 q^{40}+135 q^{38}-7 q^{36}-116 q^{34}+167 q^{32}-131 q^{30}+24 q^{28}+103 q^{26}-178 q^{24}+183 q^{22}-102 q^{20}-37 q^{18}+174 q^{16}-269 q^{14}+272 q^{12}-182 q^{10}+32 q^8+130 q^6-244 q^4+280 q^2-217+85 q^{-2} +58 q^{-4} -170 q^{-6} +191 q^{-8} -117 q^{-10} -6 q^{-12} +123 q^{-14} -165 q^{-16} +125 q^{-18} -16 q^{-20} -113 q^{-22} +195 q^{-24} -206 q^{-26} +141 q^{-28} -26 q^{-30} -88 q^{-32} +159 q^{-34} -165 q^{-36} +126 q^{-38} -55 q^{-40} -10 q^{-42} +48 q^{-44} -68 q^{-46} +60 q^{-48} -38 q^{-50} +18 q^{-52} + q^{-54} -8 q^{-56} +10 q^{-58} -10 q^{-60} +6 q^{-62} -3 q^{-64} + q^{-66}$