CFK infinity of (1,1) knots

download .nb file

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.


-- 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.