Number of components in a p,q torus link
/--
A component of a torus link
is a connected string.
-/
def torus_link_component := sorry
If you trace one line and end up visiting all positions then there is only 1 component.
Examples of torus links
T1,1 ------------------------- 1 component
T2,1
--------------
----------/--------------
---------/
1 component
T3,1
------------
------------/------------
-----------/-------------
----------/
1 component
T3,2
--------
---/--------
------------/--/---------
-----------/--/
----------/
1 component
T4,2
--------
---/--------
------------/--/---------
-----------/--/----------
----------/--/
---------/
2 components: 1 and 3 are a component. 2 and 4 are a component.
T4,2
--------
---/--------
------------/--/---------
-----------/--/----------
----------/--/
---------/
2 components: 1 and 3 are a component. 2 and 4 are a component.
How did this happen? Why not 1 component like before?
-
Do Tp,q and Tp,-q ever have a different number of components?
-
When q = 1, the first line connects with the second; When q = 2, the first line connects with the third; Generalize: The first line connects with the (q + 1)-th line; Generalize: The i-th line connects with the (q + i)-th line, if the i-th line has not been moved.