0 1 Quantum Invariants: Difference between revisions
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{{Quantum invariant table entry|knot=0_1|algebra=B2|weight=1,0}} |
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Latest revision as of 12:40, 28 June 2006
Further quantum knot invariants for 0_1.
A1 Invariants.
| Weight | Invariant |
|---|---|
| 1 | [math]\displaystyle{ q+ q^{-1} }[/math] |
| 2 | [math]\displaystyle{ q^2+1+ q^{-2} }[/math] |
| 3 | [math]\displaystyle{ q^3+q+ q^{-1} + q^{-3} }[/math] |
| 4 | [math]\displaystyle{ q^4+q^2+1+ q^{-2} + q^{-4} }[/math] |
| 5 | [math]\displaystyle{ q^5+q^3+q+ q^{-1} + q^{-3} + q^{-5} }[/math] |
| 1 | [math]\displaystyle{ q+ q^{-1} }[/math] |
| 2 | [math]\displaystyle{ q^2+1+ q^{-2} }[/math] |
| 3 | [math]\displaystyle{ q^3+q+ q^{-1} + q^{-3} }[/math] |
A2 Invariants.
| Weight | Invariant |
|---|---|
| 1,1 | [math]\displaystyle{ q^4+2 q^2+2+2 q^{-2} + q^{-4} }[/math] |
| 2,0 | [math]\displaystyle{ q^4+q^2+2+ q^{-2} + q^{-4} }[/math] |
| 3,0 | [math]\displaystyle{ q^6+q^4+2 q^2+2+2 q^{-2} + q^{-4} + q^{-6} }[/math] |
| 1,0 | Data:0 1/QuantumInvariant/A2/1,0 |
| 2,0 | [math]\displaystyle{ q^4+q^2+2+ q^{-2} + q^{-4} }[/math] |
A3 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0 | [math]\displaystyle{ q^4+q^2+2+ q^{-2} + q^{-4} }[/math] |
| 1,0,0 | [math]\displaystyle{ q^3+q+ q^{-1} + q^{-3} }[/math] |
| 1,0,1 | [math]\displaystyle{ q^6+2 q^4+3 q^2+3+3 q^{-2} +2 q^{-4} + q^{-6} }[/math] |
A4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | [math]\displaystyle{ q^6+q^4+2 q^2+2+2 q^{-2} + q^{-4} + q^{-6} }[/math] |
| 1,0,0,0 | [math]\displaystyle{ q^4+q^2+1+ q^{-2} + q^{-4} }[/math] |
B2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | [math]\displaystyle{ q^4+q^2+ q^{-2} + q^{-4} }[/math] |
| 1,0 | [math]\displaystyle{ q^6+q^2+1+ q^{-2} + q^{-6} }[/math] |
B3 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0 | [math]\displaystyle{ q^{10}+q^6+q^2+1+ q^{-2} + q^{-6} + q^{-10} }[/math] |
B4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 | [math]\displaystyle{ q^{14}+q^{10}+q^6+q^2+1+ q^{-2} + q^{-6} + q^{-10} + q^{-14} }[/math] |
B5 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0,0 | [math]\displaystyle{ q^{18}+q^{14}+q^{10}+q^6+q^2+1+ q^{-2} + q^{-6} + q^{-10} + q^{-14} + q^{-18} }[/math] |
C3 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0 | [math]\displaystyle{ q^6+q^4+q^2+ q^{-2} + q^{-4} + q^{-6} }[/math] |
C4 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0 | [math]\displaystyle{ q^8+q^6+q^4+q^2+ q^{-2} + q^{-4} + q^{-6} + q^{-8} }[/math] |
C5 Invariants.
| Weight | Invariant |
|---|---|
| 1,0,0,0,0 | [math]\displaystyle{ q^{10}+q^8+q^6+q^4+q^2+ q^{-2} + q^{-4} + q^{-6} + q^{-8} + q^{-10} }[/math] |
D4 Invariants.
| Weight | Invariant |
|---|---|
| 0,1,0,0 | [math]\displaystyle{ q^{10}+q^8+3 q^6+3 q^4+4 q^2+4+4 q^{-2} +3 q^{-4} +3 q^{-6} + q^{-8} + q^{-10} }[/math] |
| 1,0,0,0 | [math]\displaystyle{ q^6+q^4+q^2+2+ q^{-2} + q^{-4} + q^{-6} }[/math] |
G2 Invariants.
| Weight | Invariant |
|---|---|
| 0,1 | [math]\displaystyle{ q^{18}+q^{12}+q^{10}+q^8+q^6+q^2+2+ q^{-2} + q^{-6} + q^{-8} + q^{-10} + q^{-12} + q^{-18} }[/math] |
| 1,0 | [math]\displaystyle{ q^{10}+q^8+q^2+1+ q^{-2} + q^{-8} + q^{-10} }[/math] |
