Alexander Stoimenow

Some programs

Here is C++ source code of some programs. My programs require the GNU C++ compiler g++ (version 2.7.2 f.) and a UNIX shell. Since even the GNU compiler does not always handle correctly templates and offers internal compiler errors, I cant exclude funny results. Please report any errors and problems you have!

A program for solid torus invariants and PostScript images

Here is a gzipped tar-file

gsinv.tgz

of some programs which can be used to calculate the Fiedler solid torus invariants, generate PostScript images of knots, links, and tangles (1/10 in size of those rendered by KnotScape and 1/100 of those rendered by the Adobe Illustrator), and convert between different formats (including the one of KnotScape's editor).

More information on what the programs do and instructions how they are to be used may be found in the paper

Th. Fiedler and A. Stoimenow, New knot and link invariants, Proceedings of the International Conference on Knot Theory "Knots in Hellas, 98", Series on Knots and Everything 24, World Scientific, 2000.

The following papers and monographs use essentially calculations with these programs:

Th. Fiedler, Gauss Diagram Invariants for Knots and Links, Kluwer Academic Publishers, Mathematics and Its Applications Vol 532 (2001).
Th. Fiedler, Gauss diagram invariants for knots which are not closed braids, Math. Proc. Cambridge Philos. Soc. 135(2) (2003), 335--348.
A. Stoimenow, Mutant links distinguished by degree 3 Gauss sums, Proceedings of the International Conference on Knot Theory "Knots in Hellas, 98", Series on Knots and Everything 24, World Scientific, 2000.

Remarks:

Compiling the main program may, however, take several minutes.
To run the program lsd2sp requires also GNU's AWK program gawk installed on your system.

Odd crossing amphicheiral knots

A tar-file with 5 programs (and several input/data files) written for calculations in the proof of the odd crossing amphicheiral knots.

oddach.tar

The test messages what is computed compare well (not perfectly) to this version of the paper.

Program aqv23tst7.C is for $15+4k$ crossings (though it was updated to subsume the step of Jones polynomial calculation explained in the paper). Programs aqv23tst8*.C are for $17+4k$ crossings.

Compiling with g++ on UNIX and calling the program without any argument should work (though some programs give no output, because there are no diagrams of the sought type). There are some comments in the programs, but better let me know if you like to try them out. So far I give no detailed explanation, since I'm not sure who will be interested...

Hoste's conjecture for 2-bridge knots

h2br_m2.nb, MATHEMATICA notebook with complete calculation (compiled with version 10.2). Contains comments and some extraneous calculations. (If you follow the comments you will be able to redo all needed calculations, although a bit of fiddling may be necessary.)

alpha_bd.m, and almax_bd_7a.m, two data files which can be read in from the notebook file to avoid the most time consuming parts of the calculation.

h2br_m2.pdf and h2br_m2.ps.gz, printouts of the MATHEMATICA notebook (with full graphics). PS is compressed because it's 63M.

h2br3a.ps and h2br3a.pdf, draft of the paper, not in publication-ready form, but with full explanation of all details of the calculation. Comments in the MATHEMATICA notebook refer to this draft.

Alexander Stoimenow,
stoimeno_stoimenov.net