10 120

From Knot Atlas
Jump to: navigation, search

10 119.gif

10_119

10 121.gif

10_121

Contents

10 120.gif
(KnotPlot image)

See the full Rolfsen Knot Table.

Visit 10 120's page at the Knot Server (KnotPlot driven, includes 3D interactive images!)

Visit 10 120 at Knotilus!


Consists of two trefoils on a closed loop, where the trefoils are interlinked with each other. (See also 8 15.)


Symmetrical depiction.
Symmetrical depiction using only circular arcs, and lines which are horizontal, vertical, or at a 45° angle.
Alternate depiction.
Knotscape.
Simple square depiction.
Alternate square depiction.

Knot presentations

Planar diagram presentation X1627 X5,18,6,19 X13,20,14,1 X11,16,12,17 X3,10,4,11 X7,12,8,13 X9,4,10,5 X15,8,16,9 X19,14,20,15 X17,2,18,3
Gauss code -1, 10, -5, 7, -2, 1, -6, 8, -7, 5, -4, 6, -3, 9, -8, 4, -10, 2, -9, 3
Dowker-Thistlethwaite code 6 10 18 12 4 16 20 8 2 14
Conway Notation [8*20::20]


Minimum Braid Representative A Morse Link Presentation An Arc Presentation
BraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart1.gifBraidPart0.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart2.gifBraidPart1.gifBraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart0.gifBraidPart0.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart1.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart4.gifBraidPart3.gifBraidPart3.gifBraidPart0.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart2.gifBraidPart3.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart4.gifBraidPart3.gif
BraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart0.gifBraidPart4.gif

Length is 14, width is 5,

Braid index is 5

10 120 ML.gif 10 120 AP.gif
[{13, 6}, {2, 11}, {7, 12}, {5, 1}, {6, 4}, {10, 5}, {11, 9}, {8, 10}, {9, 13}, {3, 7}, {4, 8}, {12, 2}, {1, 3}]

[edit Notes on presentations of 10 120]


Three dimensional invariants

Symmetry type Reversible
Unknotting number \{2,3\}
3-genus 2
Bridge index 3
Super bridge index Missing
Nakanishi index 1
Maximal Thurston-Bennequin number [-15][3]
Hyperbolic Volume 16.2714
A-Polynomial See Data:10 120/A-polynomial

[edit Notes for 10 120's three dimensional invariants]

Four dimensional invariants

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

[edit Notes for 10 120's four dimensional invariants]

Polynomial invariants

Alexander polynomial 8 t^2-26 t+37-26 t^{-1} +8 t^{-2}
Conway polynomial 8 z^4+6 z^2+1
2nd Alexander ideal (db, data sources) \{1\}
Determinant and Signature { 105, -4 }
Jones polynomial  q^{-2} -4 q^{-3} +10 q^{-4} -13 q^{-5} +17 q^{-6} -18 q^{-7} +16 q^{-8} -13 q^{-9} +8 q^{-10} -4 q^{-11} + q^{-12}
HOMFLY-PT polynomial (db, data sources) a^{12}-4 z^2 a^{10}-3 a^{10}+3 z^4 a^8+3 z^2 a^8+4 z^4 a^6+7 z^2 a^6+3 a^6+z^4 a^4
Kauffman polynomial (db, data sources) z^6 a^{14}-2 z^4 a^{14}+z^2 a^{14}+4 z^7 a^{13}-10 z^5 a^{13}+8 z^3 a^{13}-2 z a^{13}+6 z^8 a^{12}-13 z^6 a^{12}+6 z^4 a^{12}+z^2 a^{12}+a^{12}+3 z^9 a^{11}+7 z^7 a^{11}-33 z^5 a^{11}+29 z^3 a^{11}-8 z a^{11}+16 z^8 a^{10}-33 z^6 a^{10}+17 z^4 a^{10}-7 z^2 a^{10}+3 a^{10}+3 z^9 a^9+16 z^7 a^9-44 z^5 a^9+26 z^3 a^9-4 z a^9+10 z^8 a^8-9 z^6 a^8-3 z^4 a^8+13 z^7 a^7-17 z^5 a^7+5 z^3 a^7+2 z a^7+10 z^6 a^6-11 z^4 a^6+7 z^2 a^6-3 a^6+4 z^5 a^5+z^4 a^4
The A2 invariant q^{38}+q^{36}-3 q^{34}+q^{32}-5 q^{28}+2 q^{26}-2 q^{24}+q^{22}+2 q^{20}-q^{18}+5 q^{16}-2 q^{14}+2 q^{12}+3 q^{10}-3 q^8+q^6
The G2 invariant q^{190}-3 q^{188}+8 q^{186}-16 q^{184}+21 q^{182}-23 q^{180}+9 q^{178}+25 q^{176}-74 q^{174}+131 q^{172}-159 q^{170}+124 q^{168}-16 q^{166}-151 q^{164}+326 q^{162}-410 q^{160}+358 q^{158}-152 q^{156}-149 q^{154}+426 q^{152}-569 q^{150}+496 q^{148}-227 q^{146}-123 q^{144}+405 q^{142}-489 q^{140}+345 q^{138}-47 q^{136}-260 q^{134}+434 q^{132}-410 q^{130}+162 q^{128}+180 q^{126}-491 q^{124}+639 q^{122}-549 q^{120}+251 q^{118}+157 q^{116}-531 q^{114}+731 q^{112}-704 q^{110}+430 q^{108}-19 q^{106}-371 q^{104}+597 q^{102}-569 q^{100}+321 q^{98}+41 q^{96}-335 q^{94}+427 q^{92}-308 q^{90}+21 q^{88}+288 q^{86}-464 q^{84}+445 q^{82}-224 q^{80}-79 q^{78}+349 q^{76}-482 q^{74}+440 q^{72}-267 q^{70}+46 q^{68}+153 q^{66}-266 q^{64}+286 q^{62}-215 q^{60}+119 q^{58}-14 q^{56}-56 q^{54}+84 q^{52}-91 q^{50}+68 q^{48}-38 q^{46}+13 q^{44}+7 q^{42}-12 q^{40}+12 q^{38}-10 q^{36}+6 q^{34}-3 q^{32}+q^{30}