-homology of the (6,5)-torus knot:

q \ t	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19
-78																				1
-76																			1
-74																		1	1
-72																	2	1	1 1 1
-70															1		2 1	2 1
-68													1		2	1	1 3	2
-66													2		1 3	4	1	1 1
-64											1		2 1	4	2	3 1	1
-62											1	2	2	5 1	1 1	1 1	1
-60									1	1	1	5	1	1 1 3	2
-58									1	4		3 2	3	1	1
-56								2	1	4 1	1	1 2	3
-54						1		3	1	1 2	3		1
-52						2		1 1	3	1	1
-50				1		1 1	2		3
-48				1	1	1	2		1
-46				1	2		1
-44			1		1
-42	1		1
-40	1
-38	1

Computed in six minutes on an AMD Opteron, 2.2 GHz, using 80 MB of RAM.
Diagram drawn with the KnotTheory` package for Mathematica.

For details, see my paper -foam homology calculations: arxiv.org/abs/1212.2553.

Download

foamho-1.1.tar.gz containing the source code and installation instructions in the README file. To compile, you will need at least the MPIR library, which is used for rational and integral arbitrary precision arithmetic. Optionally, the PARI library is used to obtain Smith normal forms (not necessary if you only want to compute rational homology), and the procps library to display memory consumption (on Linux only).

foamho.exe, a Windows executable compiled using MinGW running on Windows XP. No additional libraries necessary, but it is not guaranteed to work on your system.

foamho, a Linux executable. No additional libraries are necessary, but it is not guaranteed to work on your system.

Old version (1.0): foamho-1.0.tar.gz, foamho.exe, foamho.

Some results

• Unreduced sl3-homology of knots with up to 12 crossings
• Reduced sl3-homology of knots with up to 12 crossings
• Unreduced sl3-homology of links with up to 11 crossings

Let us list all knots with up to twelve crossings for which the - and -concordance invariants differ (click on the knot to see its diagram on the Knot Atlas or on KnotInfo). In our normalization, both invariants have a value of 2 for the right-handed trefoil knot.