| name: | 5_1
|
| category: | 5 |
| knot_atlas: | 5.1
|
| alternating: | Y |
| name_rank: | 4 |
| dt_name: | 5a_2 |
| dt_rank: | 5 |
| dt_notation: | [6, 8, 10, 2, 4] |
| classical_conway_name: | 5_1 |
| conway_notation: | [5] |
| two_bridge_notation: | [5,1] |
| fibered: | Y |
| gauss_notation: | {-1, 2, -3, 4, -5, 1, -2, 3, -4, 5} |
| pd_notation: | [[2,8,3,7],[4,10,5,9],[6,2,7,1],[8,4,9,3],[10,6,1,5]] |
| crossing_number: | 5 |
| tetrahedral_census_name: | [[2, 3], not hyperbolic, T(2,5)] |
| unknotting_number: | 2 |
| three_genus: | 2 |
| crosscap_number: | 1 |
| bridge_index: | 2 |
| braid_index: | 2 |
| braid_length: | 5 |
| braid_notation: | {1,1,1,1,1} |
| signature: | -4 |
| nakanishi_index: | 1 |
| super_bridge_index: | 4 |
| thurston_bennequin_number: | [3][-10] |
| arc_index: | 7 |
| polygon_index: | 8 |
| tunnel_number: | 1 |
| morse_novikov_number: | 0 |
| alexander_polynomial: | 1-t+t^2-t^3+t^4 |
| alexander_polynomial_vector: | {0, 4, 1, -1, 1, -1, 1} |
| jones_polynomial: | t^2+ t^4-t^5+ t^6-t^7 |
| jones_polynomial_vector: | {2, 7, 1, 0, 1, -1, 1, -1} |
| conway_polynomial: | 1+3*z^2+z^4 |
| conway_polynomial_vector: | {0, 2, 1, 3, 1} |
| homfly_polynomial_vector: | {0, 2, {2, 3, 3, -2}, {2, 3, 4, -1}, {2, 2, 1}} |
| kauffman_polynomial: | (2*a^(-6)+3*a^(-4))*z^(0)+(a^(-9)-a^(-7)-2*a^(-5))*z^(1)+(a^(-8)-3*a^(-6)-4*a^(-4))*z^(2)+(a^(-7)+a^(-5))*z^(3)+(a^(-6)+a^(-4))*z^(4) |
| kauffman_polynomial_vector: | {0, 4, {-6, -4, 2, 0, 3}, {-9, -5, 1, 0, -1, 0, -2}, {-8, -4, 1, 0, -3, 0, -4}, {-7, -5, 1, 0, 1}, {-6, -4, 1, 0, 1}} |
| a_polynomial: | table of A-polys
|
| smooth_four_genus: | 2 |
| topological_four_genus: | 2 |
| smooth_4d_crosscap_number: | 1 |
| topological_4d_crosscap_number: | 1 |
| smooth_concordance_genus: | 2 |
| 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: | 5 |
| seifert_matrix: | [[ -1, -1, 0, -1], [ 0, -1, 0, 0], [ -1, -1, -1, -1], [ 0, -1, 0, -1]] |
| rasmussen_invariant: | 4 |
| ozsvath_szabo_tau_invariant: | 2 |
| volume: | 0 |
| maximum_cusp_volume: | Not Hyperbolic |
| longitude_translation: | Not Hyperbolic |
| meridian_translation: | Not Hyperbolic |
| longitude_length: | Not Hyperbolic |
| meridian_length: | Not Hyperbolic |
| other_short_geodesics: | NULL |
| symmetry_type: | reversible |
| full_symmetry_group: | Z2 |
| chern_simons_invariant: | Not Hyperbolic |
| volume_imaginary_part: | Not Hyperbolic |
| arf_invariant: | 1 |
| turaev_genus: | 0 |
| signature_function: | {{0.2, {0, -1, -2}, 1}, {0.6, {-2, -3, -4}, 1}}
|
| monodromy: | abcd |
| small_large: | Small |
| positive_braid: | Y |
| positive: | Y |
| strongly_quasipositive: | Y |
| quasipositive: | Y |
| positive_braid_notation: | {1,1,1,1,1} |
| positive_pd_notation: | {{2,8,3,7},{4,10,5,9},{6,2,7,1},{8,4,9,3},{10,6,1,5}} |
| strongly_quasipositive_braid_notation: | {1,1,1,1,1} |
| quasipositive_braid_notation: | {1,1,1,1,1} |
| fd_clasp_number: | 2 |
| width: | 8 |
| torsion_numbers: | {{2,{5}}, {3,{1}}, {4,{5}}, {5,{2,2,2,2}}, {6,{5}}, {7,{1}}, {8,{5}}, {9,{1}}} |
| td_clasp_number: | 2 |
| l_space: | Yes |
| nu: | {2,-2} |
| epsilon: | 1 |
| quasi_alternating: | Y |
| almost_alternating: | N |
| adequate: | Y |
| montesinos_notation: | K(1/5) |
| boundary_slopes: | {0,10} |
| pretzel_notation: | P(-1,-1,-1,-1,-1) |
| double_slice_genus: | 4 |
| unknotting_number_algebraic: | 2 |
| khovanov_unreduced_integral_polynomial: | q^(3) + q^(5) + t^(2) q^(7) + t^(3) q^(11) + t^(4) q^(11) + t^(5) q^(15) + t^(3) q^(9) T^(2) + t^(5) q^(13) T^(2) |
| khovanov_unreduced_integral_vector: | [[0, 1, 0, 3], [0, 1, 0, 5], [0, 1, 2, 7], [0, 1, 3, 11], [0, 1, 4, 11], [0, 1, 5, 15], [2, 1, 3, 9], [2, 1, 5, 13]] |
| khovanov_reduced_integral_polynomial: | q^(4) + t^(2) q^(8) + t^(3) q^(10) + t^(4) q^(12) + t^(5) q^(14) |
| khovanov_reduced_integral_vector: | [[0, 1, 0, 4], [0, 1, 2, 8], [0, 1, 3, 10], [0, 1, 4, 12], [0, 1, 5, 14]] |
| khovanov_reduced_rational_polynomial: | q^(4) + t^(2) q^(8) + t^(3) q^(10) + t^(4) q^(12) + t^(5) q^(14) |
| khovanov_reduced_rational_vector: | [[1, 1, 0, 4], [1, 1, 2, 8], [1, 1, 3, 10], [1, 1, 4, 12], [1, 1, 5, 14]] |
| khovanov_reduced_mod2_polynomial: | q^(4) + t^(2) q^(8) + t^(3) q^(10) + t^(4) q^(12) + t^(5) q^(14) |
| khovanov_reduced_mod2_vector: | [[2, 1, 0, 4], [2, 1, 2, 8], [2, 1, 3, 10], [2, 1, 4, 12], [2, 1, 5, 14]] |
| khovanov_odd_integral_polynomial: | q^(4) + t^(2) q^(8) + t^(3) q^(10) + t^(4) q^(12) + t^(5) q^(14) |
| khovanov_odd_integral_vector: | [[0, 1, 0, 4], [0, 1, 2, 8], [0, 1, 3, 10], [0, 1, 4, 12], [0, 1, 5, 14]] |
| khovanov_odd_rational_polynomial: | q^(4) + t^(2) q^(8) + t^(3) q^(10) + t^(4) q^(12) + t^(5) q^(14) |
| khovanov_odd_rational_vector: | [[1, 1, 0, 4], [1, 1, 2, 8], [1, 1, 3, 10], [1, 1, 4, 12], [1, 1, 5, 14]] |
| khovanov_odd_mod2_polynomial: | q^(4) + t^(2) q^(8) + t^(3) q^(10) + t^(4) q^(12) + t^(5) q^(14) |
| khovanov_odd_mod2_vector: | [[2, 1, 0, 4], [2, 1, 2, 8], [2, 1, 3, 10], [2, 1, 4, 12], [2, 1, 5, 14]] |
| hfk_polynomial: | 1a^(-2)m^(-4)+ 1a^(-1)m^(-3)+ 1a^(0)m^(-2)+ 1a^(1)m^(-1)+ 1a^(2)m^(0) |
| hfk_polynomial_vector: | [1,-2,-4;1,-1,-3;1,0,-2;1,1,-1;1,2,0] |
| mosaic_tile_number: | { 5 , 17 } |
| ropelength: | 47.2016 |
| homfly_polynomial: | (3*v^4-2*v^6)+(4*v^4-v^6)*z^2+v^4*z^4 |
| grid_notation: | [[1,1],[1,3],[2,2],[2,4],[3,3],[3,5],[4,4],[4,6],[5,5],[5,7],[6,1],[6,6],[7,2],[7,7]] |
| almost_strongly_qp: | N |
| almost_strongly_qp_braid: | NULL |
| ribbon_number: | D.N.E. |
| geometric_type: | torus knot T(2,5) |
| cosmetic_crossing: | N |
