| name: | L4a1{0}
|
| name_unoriented: | L4a1 |
| category: | 4 |
| alternating: | Y |
| orientation: | {0} |
| name_rank: | 3 |
| unoriented_name_rank: | 2 |
| gauss_notation: | {{1, -3, 2, -4}, {3, -1, 4, -2}} |
| pd_notation_vector: | {{6, 1, 7, 2}, {8, 3, 5, 4}, {2, 5, 3, 6}, {4, 7, 1, 8}} |
| pd_notation_math: | PD[X[6, 1, 7, 2], X[8, 3, 5, 4], X[2, 5, 3, 6], X[4, 7, 1, 8]] |
| crossing_number: | 4 |
| braid_index: | 3 |
| braid_notation: | {3, {-2, -2, -1, 2, -1}} |
| quasi_positive_braid: | {M,2,{-1,2,1},1} |
| multivariable_alexander: | -t1-t2 |
| conway_polynomial: | -2*z |
| jones_polynomial: | -x^(-9)-x^(-5) + x^(-3)-x^(-1) |
| jones_polynomial_vector: | {-9, -1, -1, 0, 0, 0, -1, 0, 1, 0, -1} |
| homflypt_polynomial: | 1/(v^5*z)-1/(v^3*z)-z/v^3-z/v |
| homflypt_polynomial_vector: | {-1, 1, {-5, -3, 1, 0, -1}, {0, 0, 0}, {-3, -1, -1, 0, -1}} |
| kauffman_polynomial: | -a^4 + a^3/z + a^5/z + a*z-2*a^3*z-3*a^5*z + a^2*z^2 + a^4*z^2 + a^3*z^3 + a^5*z^3 |
| kauffman_polynomial_vector: | {-1, 3, {3, 5, 1, 0, 1}, {4, 4, -1}, {1, 5, 1, 0, -2, 0, -3}, {2, 4, 1, 0, 1}, {3, 5, 1, 0, 1}} |
| khovanov_polynomial: | 1 + q^(-2) + 1/(q^10*t^4) + 1/(q^8*t^4) + 1/(q^6*t^2) + 1/(q^2*t) |
| khovanov_polynomial_vector: | {-10, 0, {-4, -4, 1}, {0, 0, 0}, {-4, -4, 1}, {0, 0, 0}, {-2, -2, 1}, {0, 0, 0}, {0, 0, 0}, {0, 0, 0}, {-1, 0, 1, 1}, {0, 0, 0}, {0, 0, 1}} |
| arc_notation: | {{6, 4}, {3, 5}, {4, 2}, {1, 3}, {2, 6}, {5, 1}} |
| linking_matrix: | {{0, -2}, {-2, 0}} |
| rolfsen_name: | 4^2_1 |
| volume: | 0 |
| components: | 2 |
| dt_code: | [{6, 8}, {2, 4}] |
| arf_invariant: | 0 |
| smooth_four_genus: | 0 |
| topological_four_genus: | 0 |
| seifert_matrix: | {{0, 0, -1, 0, 0}, {0, 1, 0, 0, -1}, {0, -1, 1, 0, 0}, {0, 0, -1, 1, 1}, {0, 0, 0, 0, 0}} |
| splitting_number: | 2 |
| determinant: | 4 |
| signature: | 1 |
| nullity: | 0 |
| unlinking_number: | 2 |
| weak_splitting_number: | 2 |
