| name: | 6_1
|
| category: | 6 |
| knot_atlas: | 6.1
|
| alternating: | Y |
| name_rank: | 6 |
| dt_name: | 6a_3 |
| dt_rank: | 8 |
| dt_notation: | [4, 8, 12, 10, 2, 6] |
| classical_conway_name: | 6_1 |
| conway_notation: | [42] |
| two_bridge_notation: | [9,4] |
| fibered: | N |
| gauss_notation: | {1, -2, 3, -4, 2, -1, 5, -6, 4, -3, 6, -5} |
| pd_notation: | [[1,7,2,6],[3,10,4,11],[5,3,6,2],[7,1,8,12],[9,4,10,5],[11,9,12,8]] |
| crossing_number: | 6 |
| tetrahedral_census_name: | [4, K4_1, m032] |
| unknotting_number: | 1 |
| three_genus: | 1 |
| crosscap_number: | 2 |
| bridge_index: | 2 |
| braid_index: | 4 |
| braid_length: | 7 |
| braid_notation: | {1,1,2,-1,-3,2,-3} |
| signature: | 0 |
| nakanishi_index: | 1 |
| super_bridge_index: | [3,4] |
| thurston_bennequin_number: | [-3][-5] |
| arc_index: | 8 |
| polygon_index: | 8 |
| tunnel_number: | 1 |
| morse_novikov_number: | 2 |
| alexander_polynomial: | 2-5*t+2*t^2 |
| alexander_polynomial_vector: | {0, 2, 2, -5, 2} |
| jones_polynomial: | t^(-2)-t^(-1)+ 2-2*t+ t^2-t^3+ t^4 |
| jones_polynomial_vector: | {-2, 4, 1, -1, 2, -2, 1, -1, 1} |
| conway_polynomial: | 1-2*z^2 |
| conway_polynomial_vector: | {0, 1, 1, -2} |
| homfly_polynomial_vector: | {0, 1, {-1, 2, 1, 0, -1, 1}, {0, 1, -1, -1}} |
| kauffman_polynomial: | (a^(-4)+a^(-2)-a^2)*z^(0)+(2*a^(-3)+2*a^(-1))*z^(1)+(-3*a^(-4)-4*a^(-2)+a^2)*z^(2)+(-3*a^(-3)-2*a^(-1)+a)*z^(3)+(a^(-4)+2*a^(-2)+1)*z^(4)+(a^(-3)+a^(-1))*z^(5) |
| kauffman_polynomial_vector: | {0, 5, {-4, 2, 1, 0, 1, 0, 0, 0, -1}, {-3, -1, 2, 0, 2}, {-4, 2, -3, 0, -4, 0, 0, 0, 1}, {-3, 1, -3, 0, -2, 0, 1}, {-4, 0, 1, 0, 2, 0, 1}, {-3, -1, 1, 0, 1}} |
| a_polynomial: | table of A-polys
|
| smooth_four_genus: | 0 |
| topological_four_genus: | 0 |
| smooth_4d_crosscap_number: | 1 |
| topological_4d_crosscap_number: | 0 |
| smooth_concordance_genus: | 0
|
| topological_concordance_genus: | NULL |
| smooth_concordance_crosscap_number: | NULL |
| topological_concordance_crosscap_number: | NULL |
| algebraic_concordance_order: | 1 |
| smooth_concordance_order: | 1 |
| topological_concordance_order: | 1 |
| ribbon: | NULL |
| determinant: | 9 |
| seifert_matrix: | [[ 1, 0], [ 1, -2]] |
| rasmussen_invariant: | 0 |
| ozsvath_szabo_tau_invariant: | 0 |
| volume: | 3.163963229 |
| maximum_cusp_volume: | 1.995452053 |
| longitude_translation: | (3.927886928, 0) |
| meridian_translation: | (0.723661339, 1.016043532) |
| longitude_length: | 3.927886928 |
| meridian_length: | 1.247409392 |
| other_short_geodesics: | [(1, 1, 3.361458922), (2, 1, 3.20664573), (3, 1, 3.5182109040)] |
| symmetry_type: | reversible |
| full_symmetry_group: | D2 |
| chern_simons_invariant: | 0.155977017 |
| volume_imaginary_part: | 3.078862902 |
| arf_invariant: | 0 |
| turaev_genus: | 0 |
| signature_function: | {0}
|
| monodromy: | Not Fibered |
| small_large: | Small |
| positive_braid: | N |
| positive: | N |
| strongly_quasipositive: | N |
| quasipositive: | N |
| positive_braid_notation: | does not exist |
| positive_pd_notation: | does not exist |
| strongly_quasipositive_braid_notation: | does not exist |
| quasipositive_braid_notation: | does not exist |
| fd_clasp_number: | 0 |
| width: | 8 |
| torsion_numbers: | {{2,{9}}, {3,{7,7}}, {4,{5,45}}, {5,{31,31}}, {6,{21,189}}, {7,{127,127}}, {8,{85,765}}, {9,{511,511}}} |
| td_clasp_number: | 1 |
| l_space: | No |
| nu: | {0,0} |
| epsilon: | 0 |
| quasi_alternating: | Y |
| almost_alternating: | N |
| adequate: | Y |
| montesinos_notation: | K(4/9) |
| boundary_slopes: | {-4,0,8} |
| pretzel_notation: | P(-1,-1,-4) |
| double_slice_genus: | 1 |
| unknotting_number_algebraic: | 1 |
| khovanov_unreduced_integral_polynomial: | t^(-2) q^(-5) + t^(-1) q^(-1) + 2 q^(-1) + q + t q + t q^(3) + t^(2) q^(5) + t^(3) q^(5) + t^(4) q^(9) + t^(-1) q^(-3) T^(2) + t q T^(2) + t^(2) q^(3) T^(2) + t^(4) q^(7) T^(2) |
| khovanov_unreduced_integral_vector: | [[0, 1, -2, -5], [0, 1, -1, -1], [0, 2, 0, -1], [0, 1, 0, 1], [0, 1, 1, 1], [0, 1, 1, 3], [0, 1, 2, 5], [0, 1, 3, 5], [0, 1, 4, 9], [2, 1, -1, -3], [2, 1, 1, 1], [2, 1, 2, 3], [2, 1, 4, 7]] |
| khovanov_reduced_integral_polynomial: | t^(-2) q^(-4) + t^(-1) q^(-2) + 2 + 2 t q^(2) + t^(2) q^(4) + t^(3) q^(6) + t^(4) q^(8) |
| khovanov_reduced_integral_vector: | [[0, 1, -2, -4], [0, 1, -1, -2], [0, 2, 0, 0], [0, 2, 1, 2], [0, 1, 2, 4], [0, 1, 3, 6], [0, 1, 4, 8]] |
| khovanov_reduced_rational_polynomial: | t^(-2) q^(-4) + t^(-1) q^(-2) + 2 + 2 t q^(2) + t^(2) q^(4) + t^(3) q^(6) + t^(4) q^(8) |
| khovanov_reduced_rational_vector: | [[1, 1, -2, -4], [1, 1, -1, -2], [1, 2, 0, 0], [1, 2, 1, 2], [1, 1, 2, 4], [1, 1, 3, 6], [1, 1, 4, 8]] |
| khovanov_reduced_mod2_polynomial: | t^(-2) q^(-4) + t^(-1) q^(-2) + 2 + 2 t q^(2) + t^(2) q^(4) + t^(3) q^(6) + t^(4) q^(8) |
| khovanov_reduced_mod2_vector: | [[2, 1, -2, -4], [2, 1, -1, -2], [2, 2, 0, 0], [2, 2, 1, 2], [2, 1, 2, 4], [2, 1, 3, 6], [2, 1, 4, 8]] |
| khovanov_odd_integral_polynomial: | t^(-2) q^(-4) + t^(-1) q^(-2) + 2 + 2 t q^(2) + t^(2) q^(4) + t^(3) q^(6) + t^(4) q^(8) |
| khovanov_odd_integral_vector: | [[0, 1, -2, -4], [0, 1, -1, -2], [0, 2, 0, 0], [0, 2, 1, 2], [0, 1, 2, 4], [0, 1, 3, 6], [0, 1, 4, 8]] |
| khovanov_odd_rational_polynomial: | t^(-2) q^(-4) + t^(-1) q^(-2) + 2 + 2 t q^(2) + t^(2) q^(4) + t^(3) q^(6) + t^(4) q^(8) |
| khovanov_odd_rational_vector: | [[1, 1, -2, -4], [1, 1, -1, -2], [1, 2, 0, 0], [1, 2, 1, 2], [1, 1, 2, 4], [1, 1, 3, 6], [1, 1, 4, 8]] |
| khovanov_odd_mod2_polynomial: | t^(-2) q^(-4) + t^(-1) q^(-2) + 2 + 2 t q^(2) + t^(2) q^(4) + t^(3) q^(6) + t^(4) q^(8) |
| khovanov_odd_mod2_vector: | [[2, 1, -2, -4], [2, 1, -1, -2], [2, 2, 0, 0], [2, 2, 1, 2], [2, 1, 2, 4], [2, 1, 3, 6], [2, 1, 4, 8]] |
| hfk_polynomial: | 2a^(-1)m^(-1)+ 5a^(0)m^(0)+ 2a^(1)m^(1) |
| hfk_polynomial_vector: | [2,-1,-1;5,0,0;2,1,1] |
| mosaic_tile_number: | { 5 , 17 } |
| ropelength: | 56.7058 |
| homfly_polynomial: | (v^(-2)-v^2+v^4)+(-1-v^2)*z^2 |
| grid_notation: | [[1,2],[1,7],[2,6],[2,8],[3,1],[3,7],[4,5],[4,8],[5,4],[5,6],[6,3],[6,5],[7,2],[7,4],[8,1],[8,3]] |
