5 2 Quantum Invariants: Difference between revisions

Latest revision as of 06:51, 17 December 2008

Further quantum knot invariants for 5_2.

A1 Invariants.

Weight	Invariant
1	$-q^{13}+q^{7}+q^{5}+q$
2	$q^{36}-q^{32}-q^{26}-q^{20}+q^{14}+q^{10}+2q^{8}+q^{2}$
3	$-q^{69}+q^{65}+q^{63}-q^{59}+q^{55}-q^{51}+q^{47}+q^{45}-q^{43}-q^{37}-2q^{35}-q^{33}-q^{31}+q^{27}+q^{21}+2q^{19}-q^{15}+q^{13}+2q^{11}+q^{9}+q^{3}$
4	$q^{112}-q^{108}-q^{106}-q^{104}+q^{102}+q^{100}+q^{98}-2q^{94}+q^{90}+q^{88}-2q^{84}-q^{82}+2q^{78}+q^{76}-q^{74}+q^{70}+2q^{68}+q^{66}-q^{64}-q^{56}-2q^{54}-q^{52}-q^{50}-q^{48}+q^{44}-q^{42}-q^{40}-q^{38}+2q^{34}-q^{30}-q^{28}+q^{26}+4q^{24}+q^{22}-q^{18}+2q^{14}+q^{12}+q^{10}+q^{4}$
5	$-q^{165}+q^{161}+q^{159}+q^{157}-q^{153}-2q^{151}-q^{149}+q^{145}+2q^{143}+q^{141}-q^{139}-2q^{137}-q^{135}+q^{133}+2q^{131}+2q^{129}-2q^{125}-3q^{123}-q^{121}+q^{119}+2q^{117}+q^{115}-2q^{113}-2q^{111}-q^{109}+q^{107}+3q^{105}+q^{103}-q^{101}-q^{99}+q^{95}+2q^{93}+q^{91}-q^{89}+q^{85}+q^{83}+q^{81}-q^{77}-q^{73}-q^{71}-q^{69}-q^{63}-2q^{61}-2q^{59}-2q^{57}+2q^{53}+q^{51}-q^{49}-2q^{47}-2q^{45}+q^{43}+3q^{41}+3q^{39}-3q^{35}-2q^{33}+3q^{29}+3q^{27}+2q^{25}-q^{21}+q^{17}+q^{15}+q^{13}+q^{11}+q^{5}$
6	$q^{228}-q^{224}-q^{222}-q^{220}+2q^{214}+2q^{212}+q^{210}-q^{206}-2q^{204}-3q^{202}+q^{198}+2q^{196}+2q^{194}+q^{192}-q^{190}-4q^{188}-2q^{186}+2q^{182}+3q^{180}+4q^{178}+q^{176}-3q^{174}-3q^{172}-3q^{170}+2q^{166}+4q^{164}+2q^{162}-2q^{160}-3q^{158}-4q^{156}-q^{154}+2q^{152}+4q^{150}+2q^{148}-q^{146}-2q^{144}-3q^{142}-q^{140}+q^{138}+3q^{136}+q^{134}-2q^{132}-2q^{130}-2q^{128}+q^{124}+2q^{122}+q^{120}-q^{118}+q^{116}+q^{114}+2q^{112}+2q^{110}+2q^{108}+q^{106}-q^{98}-q^{96}-q^{94}+q^{90}-q^{88}-q^{86}-2q^{84}-2q^{82}-2q^{80}+3q^{76}+q^{74}-2q^{70}-4q^{68}-4q^{66}-q^{64}+4q^{62}+3q^{60}+2q^{58}-2q^{56}-4q^{54}-5q^{52}-q^{50}+5q^{48}+4q^{46}+4q^{44}+q^{42}-2q^{40}-4q^{38}-2q^{36}+2q^{34}+2q^{32}+3q^{30}+2q^{28}+q^{26}-q^{24}+q^{20}+q^{16}+q^{14}+q^{12}+q^{6}$

A2 Invariants.

Weight	Invariant
0,1	$-q^{20}-q^{18}+q^{12}+q^{10}+q^{8}+q^{6}+q^{2}$
0,2	$q^{50}+q^{48}+q^{46}-q^{44}-q^{42}-q^{40}-q^{38}-q^{36}-q^{34}-q^{30}-q^{28}-q^{26}+2q^{20}+2q^{18}+2q^{16}+2q^{14}+2q^{12}+q^{10}+q^{4}$
1,0	$-q^{20}-q^{18}+q^{12}+q^{10}+q^{8}+q^{6}+q^{2}$
1,1	$q^{52}+2q^{48}-2q^{46}-2q^{42}+2q^{34}-2q^{32}-5q^{28}-4q^{24}+2q^{22}+q^{20}+2q^{18}+4q^{16}+2q^{14}+4q^{12}+2q^{8}+q^{4}$
2,0	$q^{50}+q^{48}+q^{46}-q^{44}-q^{42}-q^{40}-q^{38}-q^{36}-q^{34}-q^{30}-q^{28}-q^{26}+2q^{20}+2q^{18}+2q^{16}+2q^{14}+2q^{12}+q^{10}+q^{4}$
3,0	$-q^{90}-q^{88}-q^{86}+2q^{82}+2q^{80}+2q^{78}-q^{66}+q^{62}+2q^{60}+q^{58}-q^{54}-q^{52}-3q^{50}-4q^{48}-5q^{46}-4q^{44}-3q^{42}-2q^{40}+2q^{36}+3q^{34}+2q^{32}+3q^{30}+2q^{28}+3q^{26}+2q^{24}+q^{22}+q^{20}+2q^{18}+3q^{16}+2q^{14}+q^{6}$

A3 Invariants.

Weight	Invariant
0,0,1	$-q^{27}-q^{25}-q^{23}+q^{17}+q^{15}+q^{13}+q^{11}+q^{9}+q^{7}+q^{3}$
0,1,0	$q^{42}+q^{38}-2q^{34}-2q^{32}-2q^{30}-2q^{28}-q^{26}+q^{24}+q^{22}+2q^{20}+q^{18}+2q^{16}+q^{14}+q^{12}+2q^{10}+q^{8}+q^{4}$
1,0,0	$-q^{27}-q^{25}-q^{23}+q^{17}+q^{15}+q^{13}+q^{11}+q^{9}+q^{7}+q^{3}$
1,0,1	$q^{68}+2q^{64}-q^{60}-3q^{56}+q^{54}-q^{52}+q^{50}+3q^{48}-q^{46}+q^{44}-2q^{42}-4q^{40}-4q^{38}-4q^{36}-5q^{34}-3q^{32}-q^{30}+5q^{26}+3q^{24}+7q^{22}+6q^{20}+3q^{18}+5q^{16}+q^{14}+2q^{12}+2q^{10}+q^{6}$

A4 Invariants.

Weight	Invariant
0,0,0,1	$-q^{34}-q^{32}-q^{30}-q^{28}+q^{22}+q^{20}+q^{18}+q^{16}+q^{14}+q^{12}+q^{10}+q^{8}+q^{4}$
0,1,0,0	$q^{56}+q^{54}+q^{52}+q^{50}+q^{48}-q^{46}-3q^{44}-4q^{42}-4q^{40}-4q^{38}-3q^{36}+q^{32}+2q^{30}+3q^{28}+3q^{26}+2q^{24}+2q^{22}+2q^{20}+2q^{18}+q^{16}+2q^{14}+2q^{12}+q^{10}+q^{6}$
1,0,0,0	$-q^{34}-q^{32}-q^{30}-q^{28}+q^{22}+q^{20}+q^{18}+q^{16}+q^{14}+q^{12}+q^{10}+q^{8}+q^{4}$

A5 Invariants.

Weight	Invariant
0,0,0,0,1	$-q^{41}-q^{39}-q^{37}-q^{35}-q^{33}+q^{27}+q^{25}+q^{23}+q^{21}+q^{19}+q^{17}+q^{15}+q^{13}+q^{11}+q^{9}+q^{5}$
1,0,0,0,0	$-q^{41}-q^{39}-q^{37}-q^{35}-q^{33}+q^{27}+q^{25}+q^{23}+q^{21}+q^{19}+q^{17}+q^{15}+q^{13}+q^{11}+q^{9}+q^{5}$

A6 Invariants.

Weight	Invariant
0,0,0,0,0,1	$-q^{48}-q^{46}-q^{44}-q^{42}-q^{40}-q^{38}+q^{32}+q^{30}+q^{28}+q^{26}+q^{24}+q^{22}+q^{20}+q^{18}+q^{16}+q^{14}+q^{12}+q^{10}+q^{6}$
1,0,0,0,0,0	$-q^{48}-q^{46}-q^{44}-q^{42}-q^{40}-q^{38}+q^{32}+q^{30}+q^{28}+q^{26}+q^{24}+q^{22}+q^{20}+q^{18}+q^{16}+q^{14}+q^{12}+q^{10}+q^{6}$

B2 Invariants.

Weight	Invariant
0,1	$-q^{42}-q^{38}+q^{26}-q^{24}+q^{22}+q^{18}+q^{14}+q^{12}+q^{8}+q^{4}$
1,0	$q^{68}+q^{60}-q^{56}-q^{54}-q^{52}-q^{50}-q^{48}-q^{46}-q^{44}+q^{34}+q^{32}+q^{30}+q^{26}+q^{24}+q^{22}+q^{18}+q^{16}+q^{14}+q^{6}$

B3 Invariants.

Weight	Invariant
1,0,0	$q^{100}+q^{92}-q^{82}-q^{80}-q^{78}-q^{76}-q^{74}-q^{72}-q^{70}-q^{68}-q^{66}-q^{64}+q^{56}+q^{54}+q^{50}+q^{48}+q^{46}+q^{42}+q^{40}+q^{38}+q^{34}+q^{30}+q^{26}+q^{24}+q^{22}+q^{18}+q^{10}$

B4 Invariants.

Weight	Invariant
1,0,0,0	$q^{132}+q^{124}-q^{110}-q^{106}-q^{104}-q^{102}-q^{100}-q^{98}-q^{96}-q^{94}-q^{92}-q^{90}-q^{88}-q^{86}+q^{74}+q^{72}+q^{70}+q^{66}+q^{64}+q^{62}+q^{58}+q^{56}+q^{54}+q^{50}+q^{46}+q^{42}+q^{38}+q^{34}+q^{32}+q^{30}+q^{26}+q^{22}+q^{14}$

C3 Invariants.

Weight	Invariant
1,0,0	$-q^{58}-q^{54}-q^{48}+q^{30}+q^{26}+q^{22}+q^{20}+q^{18}+q^{16}+q^{12}+q^{10}+q^{6}$

C4 Invariants.

Weight	Invariant
1,0,0,0	$-q^{74}-q^{70}-q^{62}-q^{60}-q^{48}+q^{42}+q^{38}+q^{34}+q^{30}+q^{28}+q^{26}+q^{24}+q^{22}+q^{20}+q^{16}+q^{14}+q^{12}+q^{8}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{58}+q^{54}-q^{48}-2q^{46}-2q^{44}-2q^{42}-2q^{40}-2q^{38}+2q^{32}+q^{30}+2q^{28}+q^{26}+2q^{24}+q^{22}+q^{20}+q^{18}+q^{16}+2q^{14}+q^{12}+q^{10}+q^{6}$

G2 Invariants.

Weight

Invariant

0,1

q^{204}+q^{192}+q^{190}+q^{188}-q^{186}-q^{184}-q^{176}+q^{172}-2q^{168}-q^{166}-q^{156}+q^{154}+q^{152}+q^{142}+q^{140}+q^{138}+2q^{136}+q^{134}-q^{132}-2q^{130}-q^{122}-q^{120}-q^{118}-2q^{116}-2q^{114}-3q^{112}-2q^{110}-q^{108}-2q^{106}-2q^{104}-q^{102}-q^{100}-q^{98}-q^{96}-2q^{94}-2q^{92}+q^{88}+q^{86}+2q^{84}+q^{82}+q^{78}+2q^{74}+2q^{72}+2q^{70}+2q^{68}+3q^{66}+2q^{64}+q^{62}+q^{60}+2q^{58}+2q^{56}+q^{54}+q^{50}+3q^{48}+q^{46}+q^{36}+q^{34}+q^{32}+q^{30}+q^{18}

1,0

q^{100}+q^{96}-q^{94}-q^{92}+q^{90}-q^{88}-q^{84}-q^{82}-q^{78}-q^{76}-q^{74}-q^{72}-q^{68}-q^{66}+q^{64}+q^{60}+q^{56}+q^{54}+2q^{50}-q^{48}+2q^{46}+q^{44}+q^{40}+q^{34}+2q^{24}+q^{20}+q^{14}+q^{10}

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5 2 Quantum Invariants: Difference between revisions

Latest revision as of 06:51, 17 December 2008

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