A (1,1) knot can be parametrized by four integers (as described on page
14 here).
This file defines a
function 'CFK', which takes as
input four integers (p, q, r, s), and outputs a picture of a generating
set
of CFK infinity of K(p,q,r,s).
The file also comes with a function 'AllComplexes' which takes as input
an odd integer p, and prints as output all the complexes which are CFK
infinity of some (1,1) knot computed from a genus one Heegaard diagram
with p intersection points.
Notes
-- The output represents generators as vertices and nonzero terms of
the
differential as directed edges. Unfortunately, these directed edges
sometimes pass through intermediate vertices, creating ambiguity.
Usually it should be clear from context where the edges begin and end.
This will be corrected in an updated version.
-- A particular (1,1) knot may correspond to several sets of
parameters. Ideally,'AllComplexes' would only print each isomorphism
type of complex once.
In practice, it asks Mathematica not to print any
duplicates, but it only sees as duplicates
complexes which are vertex-order-preserving-isomorphic, so the same
picture may appear
multiple times.
-- I am indebted to Gabe Doyle, who wrote a perl program which does
similar computations, and
Jake Rasmussen, who was kind enough to share his program and related
Mathematica
files with me.