| name: | 6_3
|
| category: | 6 |
| knot_atlas: | 6.3
|
| alternating: | Y |
| name_rank: | 8 |
| dt_name: | 6a_1 |
| dt_rank: | 6 |
| dt_notation: | [4, 8, 10, 2, 12, 6] |
| classical_conway_name: | 6_3 |
| conway_notation: | [2112] |
| two_bridge_notation: | [13,5] |
| fibered: | Y |
| gauss_notation: | {-1, 2, -3, 1, -4, 5, -2, 3, -6, 4, -5, 6} |
| pd_notation: | [[4,2,5,1],[8,4,9,3],[12,9,1,10],[10,5,11,6],[6,11,7,12],[2,8,3,7]] |
| crossing_number: | 6 |
| tetrahedral_census_name: | [6, K6_43, s912] |
| unknotting_number: | 1 |
| three_genus: | 2 |
| crosscap_number: | 3 |
| bridge_index: | 2 |
| braid_index: | 3 |
| braid_length: | 6 |
| braid_notation: | {1,1,-2,1,-2,-2} |
| signature: | 0 |
| nakanishi_index: | 1 |
| super_bridge_index: | [3,4] |
| thurston_bennequin_number: | [-4][-4] |
| arc_index: | 8 |
| polygon_index: | 8 |
| tunnel_number: | 1 |
| morse_novikov_number: | 0 |
| alexander_polynomial: | 1-3*t+5*t^2-3*t^3+t^4 |
| alexander_polynomial_vector: | {0, 4, 1, -3, 5, -3, 1} |
| jones_polynomial: | -t^(-3)+ 2*t^(-2)-2*t^(-1)+ 3-2*t+ 2*t^2-t^3 |
| jones_polynomial_vector: | {-3, 3, -1, 2, -2, 3, -2, 2, -1} |
| conway_polynomial: | 1+z^2+z^4 |
| conway_polynomial_vector: | {0, 2, 1, 1, 1} |
| homfly_polynomial_vector: | {0, 2, {-1, 1, -1, 3, -1}, {-1, 1, -1, 3, -1}, {0, 0, 1}} |
| kauffman_polynomial: | (a^(-2)+3+a^2)*z^(0)+(-a^(-3)-2*a^(-1)-2*a-a^3)*z^(1)+(-3*a^(-2)-6-3*a^2)*z^(2)+(a^(-3)+a^(-1)+a+a^3)*z^(3)+(2*a^(-2)+4+2*a^2)*z^(4)+(a^(-1)+a)*z^(5) |
| kauffman_polynomial_vector: | {0, 5, {-2, 2, 1, 0, 3, 0, 1}, {-3, 3, -1, 0, -2, 0, -2, 0, -1}, {-2, 2, -3, 0, -6, 0, -3}, {-3, 3, 1, 0, 1, 0, 1, 0, 1}, {-2, 2, 2, 0, 4, 0, 2}, {-1, 1, 1, 0, 1}} |
| a_polynomial: | table of A-polys
|
| smooth_four_genus: | 1 |
| topological_four_genus: | 1 |
| smooth_4d_crosscap_number: | 2 |
| topological_4d_crosscap_number: | 2 |
| smooth_concordance_genus: | 2 |
| topological_concordance_genus: | NULL |
| smooth_concordance_crosscap_number: | NULL |
| topological_concordance_crosscap_number: | NULL |
| algebraic_concordance_order: | 2 |
| smooth_concordance_order: | 2
|
| topological_concordance_order: | 2 |
| ribbon: | NULL |
| determinant: | 13 |
| seifert_matrix: | [[ -1, 0, 0, 0], [ -1, -1, 0, 0], [ -1, -1, 1, 1], [ 0, 0, 0, 1]] |
| rasmussen_invariant: | 0 |
| ozsvath_szabo_tau_invariant: | 0 |
| volume: | 5.693021091 |
| maximum_cusp_volume: | 4.038066621 |
| longitude_translation: | (6.671139306, 0) |
| meridian_translation: | (0, 1.210607794) |
| longitude_length: | 6.671139306 |
| meridian_length: | 1.210607794 |
| other_short_geodesics: | NULL |
| symmetry_type: | fully amphicheiral |
| full_symmetry_group: | D4 |
| chern_simons_invariant: | 0 |
| volume_imaginary_part: | 0 |
| arf_invariant: | 1 |
| turaev_genus: | 0 |
| signature_function: | {0}
|
| monodromy: | abCD |
| 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: | 1 |
| width: | 8 |
| torsion_numbers: | {{2,{13}}, {3,{7,7}}, {4,{3,39}}, {5,{4,4,4,4}}, {6,{7,91}}, {7,{43,43}}, {8,{21,273}}, {9,{133,133}}} |
| td_clasp_number: | 2 |
| l_space: | No |
| nu: | {0,0} |
| epsilon: | 0 |
| quasi_alternating: | Y |
| almost_alternating: | N |
| adequate: | Y |
| montesinos_notation: | K(5/13) |
| boundary_slopes: | {-6,-2,0,2,6} |
| pretzel_notation: | P(2,1,-3,1) |
| double_slice_genus: | 2 |
| unknotting_number_algebraic: | 1 |
| khovanov_unreduced_integral_polynomial: | t^(-3) q^(-7) + t^(-2) q^(-5) + t^(-2) q^(-3) + t^(-1) q^(-3) + t^(-1) q^(-1) + 2 q^(-1) + 2 q + t q + t q^(3) + t^(2) q^(3) + t^(2) q^(5) + t^(3) q^(7) + t^(-2) q^(-5) T^(2) + t^(-1) q^(-3) T^(2) + q^(-1) T^(2) + t q T^(2) + t^(2) q^(3) T^(2) + t^(3) q^(5) T^(2) |
| khovanov_unreduced_integral_vector: | [[0, 1, -3, -7], [0, 1, -2, -5], [0, 1, -2, -3], [0, 1, -1, -3], [0, 1, -1, -1], [0, 2, 0, -1], [0, 2, 0, 1], [0, 1, 1, 1], [0, 1, 1, 3], [0, 1, 2, 3], [0, 1, 2, 5], [0, 1, 3, 7], [2, 1, -2, -5], [2, 1, -1, -3], [2, 1, 0, -1], [2, 1, 1, 1], [2, 1, 2, 3], [2, 1, 3, 5]] |
| khovanov_reduced_integral_polynomial: | t^(-3) q^(-6) + 2 t^(-2) q^(-4) + 2 t^(-1) q^(-2) + 3 + 2 t q^(2) + 2 t^(2) q^(4) + t^(3) q^(6) |
| khovanov_reduced_integral_vector: | [[0, 1, -3, -6], [0, 2, -2, -4], [0, 2, -1, -2], [0, 3, 0, 0], [0, 2, 1, 2], [0, 2, 2, 4], [0, 1, 3, 6]] |
| khovanov_reduced_rational_polynomial: | t^(-3) q^(-6) + 2 t^(-2) q^(-4) + 2 t^(-1) q^(-2) + 3 + 2 t q^(2) + 2 t^(2) q^(4) + t^(3) q^(6) |
| khovanov_reduced_rational_vector: | [[1, 1, -3, -6], [1, 2, -2, -4], [1, 2, -1, -2], [1, 3, 0, 0], [1, 2, 1, 2], [1, 2, 2, 4], [1, 1, 3, 6]] |
| khovanov_reduced_mod2_polynomial: | t^(-3) q^(-6) + 2 t^(-2) q^(-4) + 2 t^(-1) q^(-2) + 3 + 2 t q^(2) + 2 t^(2) q^(4) + t^(3) q^(6) |
| khovanov_reduced_mod2_vector: | [[2, 1, -3, -6], [2, 2, -2, -4], [2, 2, -1, -2], [2, 3, 0, 0], [2, 2, 1, 2], [2, 2, 2, 4], [2, 1, 3, 6]] |
| khovanov_odd_integral_polynomial: | t^(-3) q^(-6) + 2 t^(-2) q^(-4) + 2 t^(-1) q^(-2) + 3 + 2 t q^(2) + 2 t^(2) q^(4) + t^(3) q^(6) |
| khovanov_odd_integral_vector: | [[0, 1, -3, -6], [0, 2, -2, -4], [0, 2, -1, -2], [0, 3, 0, 0], [0, 2, 1, 2], [0, 2, 2, 4], [0, 1, 3, 6]] |
| khovanov_odd_rational_polynomial: | t^(-3) q^(-6) + 2 t^(-2) q^(-4) + 2 t^(-1) q^(-2) + 3 + 2 t q^(2) + 2 t^(2) q^(4) + t^(3) q^(6) |
| khovanov_odd_rational_vector: | [[1, 1, -3, -6], [1, 2, -2, -4], [1, 2, -1, -2], [1, 3, 0, 0], [1, 2, 1, 2], [1, 2, 2, 4], [1, 1, 3, 6]] |
| khovanov_odd_mod2_polynomial: | t^(-3) q^(-6) + 2 t^(-2) q^(-4) + 2 t^(-1) q^(-2) + 3 + 2 t q^(2) + 2 t^(2) q^(4) + t^(3) q^(6) |
| khovanov_odd_mod2_vector: | [[2, 1, -3, -6], [2, 2, -2, -4], [2, 2, -1, -2], [2, 3, 0, 0], [2, 2, 1, 2], [2, 2, 2, 4], [2, 1, 3, 6]] |
| hfk_polynomial: | 1a^(-2)m^(-2)+ 3a^(-1)m^(-1)+ 5a^(0)m^(0)+ 3a^(1)m^(1)+ 1a^(2)m^(2) |
| hfk_polynomial_vector: | [1,-2,-2;3,-1,-1;5,0,0;3,1,1;1,2,2] |
| mosaic_tile_number: | { 6 , 22 } |
| ropelength: | 57.8392 |
| homfly_polynomial: | (-v^(-2)+3-v^2)+(-v^(-2)+3-v^2)*z^2+z^4 |
| grid_notation: | [[1,1],[1,3],[2,2],[2,4],[3,3],[3,6],[4,5],[4,8],[5,1],[5,7],[6,4],[6,8],[7,2],[7,6],[8,5],[8,7]] |
