details/L4a1_0_7e067eac.json
FL expansions
| Newt(ΔL) vertex |
Exposing functional |
Leading x-power |
Leading q-power |
Inversion datum |
Inversion cycle |
FL |
(1/2, -1/2) |
(1/2, 1) |
x1^(-1/2)x2^(1/2) |
q^(-1/2) |
{"0": [-1, -1, -1, -1, -1, -1], "1": [-1, -1, -1, -1]}
|
|
(q^(89/2))*x1^(-19/2)*x2^(19/2) + (-q^(71/2))*x1^(-17/2)*x2^(17/2) + (q^(55/2))*x1^(-15/2)*x2^(15/2) + (-q^(41/2))*x1^(-13/2)*x2^(13/2) + (q^(29/2))*x1^(-11/2)*x2^(11/2) + (-q^(19/2))*x1^(-9/2)*x2^(9/2) + (q^(11/2))*x1^(-7/2)*x2^(7/2) + (-q^(5/2))*x1^(-5/2)*x2^(5/2) + (q^(1/2))*x1^(-3/2)*x2^(3/2) + (-q^(-1/2))*x1^(-1/2)*x2^(1/2)
|
(1/2, -1/2) |
(1/2, 1) |
x1^(-1/2)x2^(1/2) |
q^(-1/2) |
{"0": [1, -1, -1, -1, -1, -1], "1": [-1, -1, -1, 1]}
|
|
(q^(89/2))*x1^(-19/2)*x2^(19/2) + (-q^(71/2))*x1^(-17/2)*x2^(17/2) + (q^(55/2))*x1^(-15/2)*x2^(15/2) + (-q^(41/2))*x1^(-13/2)*x2^(13/2) + (q^(29/2))*x1^(-11/2)*x2^(11/2) + (-q^(19/2))*x1^(-9/2)*x2^(9/2) + (q^(11/2))*x1^(-7/2)*x2^(7/2) + (-q^(5/2))*x1^(-5/2)*x2^(5/2) + (q^(1/2))*x1^(-3/2)*x2^(3/2) + (-q^(-1/2))*x1^(-1/2)*x2^(1/2)
|
(1/2, -1/2) |
(1/2, 1) |
x1^(-1/2)x2^(1/2) |
q^(-1/2) |
{"0": [1, -1, -1, -1, -1, -1], "1": [-1, -1, -1, 1]}
|
|
(q^(55/2))*x1^(-15/2)*x2^(15/2) + (-q^(41/2))*x1^(-13/2)*x2^(13/2) + (q^(29/2))*x1^(-11/2)*x2^(11/2) + (-q^(19/2))*x1^(-9/2)*x2^(9/2) + (q^(11/2))*x1^(-7/2)*x2^(7/2) + (-q^(5/2))*x1^(-5/2)*x2^(5/2) + (q^(1/2))*x1^(-3/2)*x2^(3/2) + (-q^(-1/2))*x1^(-1/2)*x2^(1/2)
|
(-1/2, 1/2) |
|
x1^(1/2)x2^(-1/2) |
q^(-1/2) |
|
|
(q^(89/2))*x1^(19/2)*x2^(-19/2) + (-q^(71/2))*x1^(17/2)*x2^(-17/2) + (q^(55/2))*x1^(15/2)*x2^(-15/2) + (-q^(41/2))*x1^(13/2)*x2^(-13/2) + (q^(29/2))*x1^(11/2)*x2^(-11/2) + (-q^(19/2))*x1^(9/2)*x2^(-9/2) + (q^(11/2))*x1^(7/2)*x2^(-7/2) + (-q^(5/2))*x1^(5/2)*x2^(-5/2) + (q^(1/2))*x1^(3/2)*x2^(-3/2) + (-q^(-1/2))*x1^(1/2)*x2^(-1/2)
|
(-1/2, 1/2) |
|
x1^(1/2)x2^(-1/2) |
q^(-1/2) |
|
|
(q^(55/2))*x1^(15/2)*x2^(-15/2) + (-q^(41/2))*x1^(13/2)*x2^(-13/2) + (q^(29/2))*x1^(11/2)*x2^(-11/2) + (-q^(19/2))*x1^(9/2)*x2^(-9/2) + (q^(11/2))*x1^(7/2)*x2^(-7/2) + (-q^(5/2))*x1^(5/2)*x2^(-5/2) + (q^(1/2))*x1^(3/2)*x2^(-3/2) + (-q^(-1/2))*x1^(1/2)*x2^(-1/2)
|
Braid
| Braid word |
Components |
Crossings |
Strands |
[-2, -2, -1, 2, -1] |
2 |
5 |
3 |
Multivariable Alexander polynomial
| ΔL |
-A1^(1/2)*A2^(-1/2) - A1^(-1/2)*A2^(1/2) |
Warning: the A1, A2, … basis used for the HFL and Alexander data might not match the x1, x2, … basis used for FL.
Dual Thurston polytope
| Vertex | Dual to fibered face |
|---|
(-1, 1) |
yes |
(1, -1) |
yes |
HFL polytope
| Poincaré polynomial |
|---|
m^(-1)*A1^(-1) + m^(-1)*A2^(-1) + A1^(-1)*A2 + 2 + A1*A2^(-1) + m*A2 + m*A1 |
| Vertex | Maslov | Rank |
|---|
(-1, 0) | -1 | 1 |
(0, -1) | -1 | 1 |
(1, -1) | 0 | 1 |
(1, 0) | 1 | 1 |
(0, 1) | 1 | 1 |
(-1, 1) | 0 | 1 |
Record
FL/HFL Links
orderOption(int) |
3 |
|---|
namestring |
L4a1{0} |
|---|
statusstring |
success |
|---|
slugstring |
L4a1_0_7e067eac |
|---|
result_filestring |
details/L4a1_0_7e067eac.json |
|---|
complexity_scoreOption(int) |
32 |
|---|
strandsOption(int) |
null |
|---|
crossingsOption(int) |
4 |
|---|
component_countOption(int) |
2 |
|---|
girthOption(int) |
4 |
|---|
total_rankOption(int) |
8 |
|---|
wall_secondsOption(float) |
0.002465 |
|---|
backend_secondsOption(float) |
0.0 |
|---|
errorstring |
|
|---|
dimensionOption(int) |
2 |
|---|
support_sizeOption(int) |
7 |
|---|
vertex_countOption(int) |
6 |
|---|
fibered_vertex_countOption(int) |
2 |
|---|
polytope_statusstring |
computed |
|---|
alexander_support_sizeOption(int) |
2 |
|---|
alexander_vertex_countOption(int) |
2 |
|---|
alexander_relationstring |
not_computed |
|---|
fk_countint |
5 |
|---|
detailsRowRef(FLHFLLinks) |
{
"dataset": "FLHFLLinks",
"key": "L4a1_0_7e067eac"
} |
|---|
detail_assetstring |
/api/v1/datasets/FLHFLLinks/assets/L4a1_0_7e067eac |
|---|