# 9 43

 (KnotPlot image) See the full Rolfsen Knot Table. Visit 9 43's page at the Knot Server (KnotPlot driven, includes 3D interactive images!) Visit 9 43 at Knotilus!

### Knot presentations

 Planar diagram presentation X4251 X10,6,11,5 X8394 X2,9,3,10 X14,8,15,7 X15,1,16,18 X11,17,12,16 X17,13,18,12 X6,14,7,13 Gauss code 1, -4, 3, -1, 2, -9, 5, -3, 4, -2, -7, 8, 9, -5, -6, 7, -8, 6 Dowker-Thistlethwaite code 4 8 10 14 2 -16 6 -18 -12 Conway Notation [211,3,2-]

Minimum Braid Representative A Morse Link Presentation An Arc Presentation

Length is 9, width is 4,

Braid index is 4

[{5, 10}, {9, 1}, {10, 8}, {6, 9}, {4, 7}, {3, 6}, {2, 5}, {1, 4}, {7, 2}, {8, 3}]

### Three dimensional invariants

 Symmetry type Reversible Unknotting number 2 3-genus 3 Bridge index 3 Super bridge index ${\displaystyle \{4,5\}}$ Nakanishi index 1 Maximal Thurston-Bennequin number [1][-10] Hyperbolic Volume 5.90409 A-Polynomial See Data:9 43/A-polynomial

### Four dimensional invariants

 Smooth 4 genus ${\displaystyle 2}$ Topological 4 genus ${\displaystyle 2}$ Concordance genus ${\displaystyle 3}$ Rasmussen s-Invariant -4

### Polynomial invariants

 Alexander polynomial ${\displaystyle -t^{3}+3t^{2}-2t+1-2t^{-1}+3t^{-2}-t^{-3}}$ Conway polynomial ${\displaystyle -z^{6}-3z^{4}+z^{2}+1}$ 2nd Alexander ideal (db, data sources) ${\displaystyle \{1\}}$ Determinant and Signature { 13, 4 } Jones polynomial ${\displaystyle -q^{7}+2q^{6}-2q^{5}+2q^{4}-2q^{3}+2q^{2}-q+1}$ HOMFLY-PT polynomial (db, data sources) ${\displaystyle -z^{6}a^{-4}+z^{4}a^{-2}-5z^{4}a^{-4}+z^{4}a^{-6}+4z^{2}a^{-2}-7z^{2}a^{-4}+4z^{2}a^{-6}+3a^{-2}-4a^{-4}+3a^{-6}-a^{-8}}$ Kauffman polynomial (db, data sources) ${\displaystyle z^{7}a^{-3}+z^{7}a^{-5}+z^{6}a^{-2}+3z^{6}a^{-4}+2z^{6}a^{-6}-4z^{5}a^{-3}-3z^{5}a^{-5}+z^{5}a^{-7}-5z^{4}a^{-2}-13z^{4}a^{-4}-8z^{4}a^{-6}+3z^{3}a^{-3}+z^{3}a^{-5}-2z^{3}a^{-7}+7z^{2}a^{-2}+14z^{2}a^{-4}+9z^{2}a^{-6}+2z^{2}a^{-8}+za^{-7}+za^{-9}-3a^{-2}-4a^{-4}-3a^{-6}-a^{-8}}$ The A2 invariant ${\displaystyle 1+q^{-2}+q^{-4}+q^{-6}-2q^{-12}+q^{-18}+q^{-20}-q^{-26}}$ The G2 invariant ${\displaystyle q^{-2}+2q^{-6}-q^{-8}+q^{-10}+q^{-12}-q^{-14}+4q^{-16}-q^{-18}+2q^{-20}+q^{-22}-q^{-24}+3q^{-26}-q^{-30}+2q^{-32}-q^{-34}+2q^{-38}-3q^{-40}+2q^{-42}-2q^{-44}-q^{-48}-3q^{-50}+q^{-52}-3q^{-54}+q^{-56}-2q^{-58}-q^{-64}+q^{-66}-q^{-68}+2q^{-72}+3q^{-78}-2q^{-80}+4q^{-82}+2q^{-88}-2q^{-90}+2q^{-92}-q^{-100}-q^{-102}+q^{-104}-q^{-106}-q^{-108}-q^{-112}-q^{-116}+q^{-120}}$

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

Same Alexander/Conway Polynomial: {}

Same Jones Polynomial (up to mirroring, ${\displaystyle q\leftrightarrow q^{-1}}$): {K11n12,}

### Vassiliev invariants

 V2 and V3: (1, 2)
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 ${\displaystyle 4}$ ${\displaystyle 16}$ ${\displaystyle 8}$ ${\displaystyle {\frac {254}{3}}}$ ${\displaystyle {\frac {82}{3}}}$ ${\displaystyle 64}$ ${\displaystyle {\frac {1024}{3}}}$ ${\displaystyle {\frac {256}{3}}}$ ${\displaystyle 80}$ ${\displaystyle {\frac {32}{3}}}$ ${\displaystyle 128}$ ${\displaystyle {\frac {1016}{3}}}$ ${\displaystyle {\frac {328}{3}}}$ ${\displaystyle {\frac {37231}{30}}}$ ${\displaystyle -{\frac {154}{5}}}$ ${\displaystyle {\frac {31502}{45}}}$ ${\displaystyle {\frac {593}{18}}}$ ${\displaystyle {\frac {2671}{30}}}$

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 ${\displaystyle t^{r}q^{j}}$ are shown, along with their alternating sums ${\displaystyle \chi }$ (fixed ${\displaystyle j}$, alternation over ${\displaystyle r}$). The squares with yellow highlighting are those on the "critical diagonals", where ${\displaystyle j-2r=s+1}$ or ${\displaystyle j-2r=s-1}$, where ${\displaystyle s=}$4 is the signature of 9 43. Nonzero entries off the critical diagonals (if any exist) are highlighted in red.
 \ r \ j \
-2-1012345χ
15       1-1
13      1 1
11     11 0
9    11  0
7   11   0
5  11    0
3 12     1
1        0
-11       1
Integral Khovanov Homology
 ${\displaystyle \dim {\mathcal {G}}_{2r+i}\operatorname {KH} _{\mathbb {Z} }^{r}}$ ${\displaystyle i=3}$ ${\displaystyle i=5}$ ${\displaystyle r=-2}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=-1}$ ${\displaystyle {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=0}$ ${\displaystyle {\mathbb {Z} }^{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=1}$ ${\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=2}$ ${\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=3}$ ${\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=4}$ ${\displaystyle {\mathbb {Z} }\oplus {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$ ${\displaystyle r=5}$ ${\displaystyle {\mathbb {Z} }_{2}}$ ${\displaystyle {\mathbb {Z} }}$