| name: | 3_1
|
| category: | 3 |
| knot_atlas: | 3.1
|
| alternating: | Y |
| name_rank: | 2 |
| dt_name: | 3a_1 |
| dt_rank: | 2 |
| dt_notation: | [4, 6, 2] |
| classical_conway_name: | 3_1 |
| conway_notation: | [3] |
| two_bridge_notation: | [3,1] |
| fibered: | Y |
| gauss_notation: | {1, -2, 3, -1, 2, -3} |
| pd_notation: | [[1,5,2,4],[3,1,4,6],[5,3,6,2]] |
| crossing_number: | 3 |
| tetrahedral_census_name: | [2, not hyperbolic, T(2,3)] |
| unknotting_number: | 1 |
| three_genus: | 1 |
| crosscap_number: | 1 |
| bridge_index: | 2 |
| braid_index: | 2 |
| braid_length: | 3 |
| braid_notation: | {1,1,1} |
| signature: | -2 |
| nakanishi_index: | 1 |
| super_bridge_index: | 3 |
| thurston_bennequin_number: | [1][-6] |
| arc_index: | 5 |
| polygon_index: | 6 |
| tunnel_number: | 1 |
| morse_novikov_number: | 0 |
| alexander_polynomial: | 1-t+t^2 |
| alexander_polynomial_vector: | {0, 2, 1, -1, 1} |
| jones_polynomial: | t+ t^3-t^4 |
| jones_polynomial_vector: | {1, 4, 1, 0, 1, -1} |
| conway_polynomial: | 1+z^2 |
| conway_polynomial_vector: | {0, 1, 1, 1} |
| homfly_polynomial_vector: | {0, 1, {1, 2, 2, -1}, {1, 1, 1}} |
| kauffman_polynomial: | (-a^(-4)-2*a^(-2))*z^(0)+(a^(-5)+a^(-3))*z^(1)+(a^(-4)+a^(-2))*z^(2) |
| kauffman_polynomial_vector: | {0, 2, {-4, -2, -1, 0, -2}, {-5, -3, 1, 0, 1}, {-4, -2, 1, 0, 1}} |
| a_polynomial: | M^6 +L
|
| 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: | 3 |
| seifert_matrix: | [[ -1, 0], [ -1, -1]] |
| rasmussen_invariant: | 2 |
| ozsvath_szabo_tau_invariant: | 1 |
| 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: | {{0.3333333333, {0, -1, -2}, 1}}
|
| monodromy: | ab |
| small_large: | Small |
| positive_braid: | Y |
| positive: | Y |
| strongly_quasipositive: | Y |
| quasipositive: | Y |
| positive_braid_notation: | {1,1,1} |
| positive_pd_notation: | {{1,5,2,4},{3,1,4,6},{5,3,6,2}} |
| strongly_quasipositive_braid_notation: | {1,1,1} |
| quasipositive_braid_notation: | {1,1,1} |
| fd_clasp_number: | 1 |
| width: | 8 |
| torsion_numbers: | {{2,{3}}, {3,{2,2}}, {4,{3}}, {5,{1}}, {6,{0,0}}, {7,{1}}, {8,{3}}, {9,{2,2}}} |
| td_clasp_number: | 1 |
| l_space: | Yes |
| nu: | {1,-1} |
| epsilon: | 1 |
| quasi_alternating: | Y |
| almost_alternating: | N |
| adequate: | Y |
| montesinos_notation: | K(1/3) |
| boundary_slopes: | {0,6} |
| pretzel_notation: | P(-1,-1,-1) |
| double_slice_genus: | 2 |
| unknotting_number_algebraic: | 1 |
| khovanov_unreduced_integral_polynomial: | q + q^(3) + t^(2) q^(5) + t^(3) q^(9) + t^(3) q^(7) T^(2) |
| khovanov_unreduced_integral_vector: | [[0, 1, 0, 1], [0, 1, 0, 3], [0, 1, 2, 5], [0, 1, 3, 9], [2, 1, 3, 7]] |
| khovanov_reduced_integral_polynomial: | q^(2) + t^(2) q^(6) + t^(3) q^(8) |
| khovanov_reduced_integral_vector: | [[0, 1, 0, 2], [0, 1, 2, 6], [0, 1, 3, 8]] |
| khovanov_reduced_rational_polynomial: | q^(2) + t^(2) q^(6) + t^(3) q^(8) |
| khovanov_reduced_rational_vector: | [[1, 1, 0, 2], [1, 1, 2, 6], [1, 1, 3, 8]] |
| khovanov_reduced_mod2_polynomial: | q^(2) + t^(2) q^(6) + t^(3) q^(8) |
| khovanov_reduced_mod2_vector: | [[2, 1, 0, 2], [2, 1, 2, 6], [2, 1, 3, 8]] |
| khovanov_odd_integral_polynomial: | q^(2) + t^(2) q^(6) + t^(3) q^(8) |
| khovanov_odd_integral_vector: | [[0, 1, 0, 2], [0, 1, 2, 6], [0, 1, 3, 8]] |
| khovanov_odd_rational_polynomial: | q^(2) + t^(2) q^(6) + t^(3) q^(8) |
| khovanov_odd_rational_vector: | [[1, 1, 0, 2], [1, 1, 2, 6], [1, 1, 3, 8]] |
| khovanov_odd_mod2_polynomial: | q^(2) + t^(2) q^(6) + t^(3) q^(8) |
| khovanov_odd_mod2_vector: | [[2, 1, 0, 2], [2, 1, 2, 6], [2, 1, 3, 8]] |
| hfk_polynomial: | 1a^(-1)m^(-2)+ 1a^(0)m^(-1)+ 1a^(1)m^(0) |
| hfk_polynomial_vector: | [1,-1,-2;1,0,-1;1,1,0] |
| mosaic_tile_number: | { 4 , 12 } |
| ropelength: | 32.7436 |
| homfly_polynomial: | (2*v^2-v^4)+v^2*z^2 |
| grid_notation: | [[1,1],[1,3],[2,2],[2,4],[3,3],[3,5],[4,1],[4,4],[5,2],[5,5]] |
