| name: | 5_2
|
| category: | 5 |
| knot_atlas: | 5.2
|
| alternating: | Y |
| name_rank: | 5 |
| dt_name: | 5a_1 |
| dt_rank: | 4 |
| dt_notation: | [4, 8, 10, 2, 6] |
| classical_conway_name: | 5_2 |
| conway_notation: | [32] |
| two_bridge_notation: | [7,3] |
| fibered: | N |
| gauss_notation: | {1, -2, 3, -1, 4, -5, 2, -3, 5, -4} |
| pd_notation: | [[1,5,2,4],[3,9,4,8],[5,1,6,10],[7,3,8,2],[9,7,10,6]] |
| crossing_number: | 5 |
| tetrahedral_census_name: | [3, K3_2, m015] |
| unknotting_number: | 1 |
| three_genus: | 1 |
| crosscap_number: | 2 |
| bridge_index: | 2 |
| braid_index: | 3 |
| braid_length: | 6 |
| braid_notation: | {1,1,1,2,-1,2} |
| signature: | -2 |
| nakanishi_index: | 1 |
| super_bridge_index: | [3,4] |
| thurston_bennequin_number: | [1][-8] |
| arc_index: | 7 |
| polygon_index: | 8 |
| tunnel_number: | 1 |
| morse_novikov_number: | 2 |
| alexander_polynomial: | 2-3*t+2*t^2 |
| alexander_polynomial_vector: | {0, 2, 2, -3, 2} |
| jones_polynomial: | t-t^2+ 2*t^3-t^4+ t^5-t^6 |
| jones_polynomial_vector: | {1, 6, 1, -1, 2, -1, 1, -1} |
| conway_polynomial: | 1+2*z^2 |
| conway_polynomial_vector: | {0, 1, 1, 2} |
| homfly_polynomial_vector: | {0, 1, {1, 3, 1, 1, -1}, {1, 2, 1, 1}} |
| kauffman_polynomial: | (a^(-6)+a^(-4)-a^(-2))*z^(0)+(-2*a^(-7)-2*a^(-5))*z^(1)+(-2*a^(-6)-a^(-4)+a^(-2))*z^(2)+(a^(-7)+2*a^(-5)+a^(-3))*z^(3)+(a^(-6)+a^(-4))*z^(4) |
| kauffman_polynomial_vector: | {0, 4, {-6, -2, 1, 0, 1, 0, -1}, {-7, -5, -2, 0, -2}, {-6, -2, -2, 0, -1, 0, 1}, {-7, -3, 1, 0, 2, 0, 1}, {-6, -4, 1, 0, 1}} |
| a_polynomial: | table of A-polys
|
| smooth_four_genus: | 1 |
| topological_four_genus: | 1 |
| smooth_4d_crosscap_number: | 1 |
| topological_4d_crosscap_number: | 1 |
| smooth_concordance_genus: | 1 |
| topological_concordance_genus: | NULL |
| smooth_concordance_crosscap_number: | NULL |
| topological_concordance_crosscap_number: | NULL |
| algebraic_concordance_order: | infty |
| smooth_concordance_order: | infty |
| topological_concordance_order: | infty |
| ribbon: | NULL |
| determinant: | 7 |
| seifert_matrix: | [[ -1, -1], [ 0, -2]] |
| rasmussen_invariant: | 2 |
| ozsvath_szabo_tau_invariant: | 1 |
| volume: | 2.828122088 |
| maximum_cusp_volume: | 1.973463516 |
| longitude_translation: | (4.469301752, 0) |
| meridian_translation: | (0.738117946, 0.883119389) |
| longitude_length: | 4.469301752 |
| meridian_length: | 1.150963925 |
| other_short_geodesics: | NULL |
| symmetry_type: | reversible |
| full_symmetry_group: | D2 |
| chern_simons_invariant: | -0.153204133 |
| volume_imaginary_part: | -3.024128377 |
| arf_invariant: | 0 |
| turaev_genus: | 0 |
| signature_function: | {{0.2300534562, {0, -1, -2}, 1}}
|
| monodromy: | Not Fibered |
| small_large: | Small |
| positive_braid: | N |
| positive: | Y |
| strongly_quasipositive: | Y |
| quasipositive: | Y |
| positive_braid_notation: | does not exist |
| positive_pd_notation: | {{1,5,2,4},{3,9,4,8},{5,1,6,10},{7,3,8,2},{9,7,10,6}} |
| strongly_quasipositive_braid_notation: | {1,1,2,{2,1,-2}} |
| quasipositive_braid_notation: | {1,1,2,{2,1,-2}} |
| fd_clasp_number: | 1 |
| width: | 8 |
| torsion_numbers: | {{2,{7}}, {3,{5,5}}, {4,{3,21}}, {5,{11,11}}, {6,{5,35}}, {7,{13,13}}, {8,{3,21}}, {9,{5,5}}} |
| td_clasp_number: | 1 |
| l_space: | No |
| nu: | {1,-1} |
| epsilon: | 1 |
| quasi_alternating: | Y |
| almost_alternating: | N |
| adequate: | Y |
| montesinos_notation: | K(3/7) |
| boundary_slopes: | {0,4,10} |
| pretzel_notation: | P(-1,-1,-3) |
| double_slice_genus: | 2 |
| unknotting_number_algebraic: | 1 |
| khovanov_unreduced_integral_polynomial: | q + q^(3) + t q^(3) + t^(2) q^(5) + t^(2) q^(7) + t^(3) q^(9) + t^(4) q^(9) + t^(5) q^(13) + t^(2) q^(5) T^(2) + t^(3) q^(7) T^(2) + t^(5) q^(11) T^(2) |
| khovanov_unreduced_integral_vector: | [[0, 1, 0, 1], [0, 1, 0, 3], [0, 1, 1, 3], [0, 1, 2, 5], [0, 1, 2, 7], [0, 1, 3, 9], [0, 1, 4, 9], [0, 1, 5, 13], [2, 1, 2, 5], [2, 1, 3, 7], [2, 1, 5, 11]] |
| khovanov_reduced_integral_polynomial: | q^(2) + t q^(4) + 2 t^(2) q^(6) + t^(3) q^(8) + t^(4) q^(10) + t^(5) q^(12) |
| khovanov_reduced_integral_vector: | [[0, 1, 0, 2], [0, 1, 1, 4], [0, 2, 2, 6], [0, 1, 3, 8], [0, 1, 4, 10], [0, 1, 5, 12]] |
| khovanov_reduced_rational_polynomial: | q^(2) + t q^(4) + 2 t^(2) q^(6) + t^(3) q^(8) + t^(4) q^(10) + t^(5) q^(12) |
| khovanov_reduced_rational_vector: | [[1, 1, 0, 2], [1, 1, 1, 4], [1, 2, 2, 6], [1, 1, 3, 8], [1, 1, 4, 10], [1, 1, 5, 12]] |
| khovanov_reduced_mod2_polynomial: | q^(2) + t q^(4) + 2 t^(2) q^(6) + t^(3) q^(8) + t^(4) q^(10) + t^(5) q^(12) |
| khovanov_reduced_mod2_vector: | [[2, 1, 0, 2], [2, 1, 1, 4], [2, 2, 2, 6], [2, 1, 3, 8], [2, 1, 4, 10], [2, 1, 5, 12]] |
| khovanov_odd_integral_polynomial: | q^(2) + t q^(4) + 2 t^(2) q^(6) + t^(3) q^(8) + t^(4) q^(10) + t^(5) q^(12) |
| khovanov_odd_integral_vector: | [[0, 1, 0, 2], [0, 1, 1, 4], [0, 2, 2, 6], [0, 1, 3, 8], [0, 1, 4, 10], [0, 1, 5, 12]] |
| khovanov_odd_rational_polynomial: | q^(2) + t q^(4) + 2 t^(2) q^(6) + t^(3) q^(8) + t^(4) q^(10) + t^(5) q^(12) |
| khovanov_odd_rational_vector: | [[1, 1, 0, 2], [1, 1, 1, 4], [1, 2, 2, 6], [1, 1, 3, 8], [1, 1, 4, 10], [1, 1, 5, 12]] |
| khovanov_odd_mod2_polynomial: | q^(2) + t q^(4) + 2 t^(2) q^(6) + t^(3) q^(8) + t^(4) q^(10) + t^(5) q^(12) |
| khovanov_odd_mod2_vector: | [[2, 1, 0, 2], [2, 1, 1, 4], [2, 2, 2, 6], [2, 1, 3, 8], [2, 1, 4, 10], [2, 1, 5, 12]] |
| hfk_polynomial: | 2a^(-1)m^(-2)+ 3a^(0)m^(-1)+ 2a^(1)m^(0) |
| hfk_polynomial_vector: | [2,-1,-2;3,0,-1;2,1,0] |
| mosaic_tile_number: | { 5 , 17 } |
| ropelength: | 49.4701 |
| homfly_polynomial: | (v^2+v^4-v^6)+(v^2+v^4)*z^2 |
| grid_notation: | [[1,2],[1,6],[2,5],[2,7],[3,1],[3,6],[4,4],[4,7],[5,3],[5,5],[6,2],[6,4],[7,1],[7,3]] |
