Robert Lipshitz

Computer Code

Bordered Heegaard Floer homology

bfh_python

In a sequence of papers, Peter Ozsváth, Dylan Thurston, and I gave an algorithm for computing the Heegaard Floer invariant HF-hat of a closed 3-manifold and the Ozsváth-Szabó spectral sequence associated to a link in the 3-sphere. We also gave a computer implementation of the algorithm for computing HF-hat. In his thesis, Bohua Zhan improved the algorithm, using a notion of "local DA bimodules". He also re-implemented the original and improved algorithms, and extended the implementation to comptue the Ozsváth-Szabó spectral sequence.

Zhan's code is bfh_python, available here. If you are interested in using bordered Heegaard Floer homology for computations, you should use this.

I have written some documentation introducing bfh_python, available here. This was supported by NSF grant DMS-1810893.

Archaic code referenced in my papers

The following code is largely archaic; use bfh_python instead.

  • A technology demonstration of a package to compute Heegaard Floer invariants using bordered Floer homology is available here. This is referenced in "Computing HF-hat by factoring mapping classes".
    • You will need Sage to run this. I have not checked that it still works in current versions of Sage.
    • This is version 0.2 (August 5, 2011). It corrects several (critical) bugs found by Bohua Zhan.
    • This version contains new installation options, thanks to Nathan Dunfield. See the README (also courtesy of Dunfield).
    • Partial documentation is included, in a PDF called BordProgDocs
    • Copyright 2010-2012 Robert Lipshitz, Peter Ozsvath and Dylan Thurston.
    • This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
    • This was supported by NSF Grant DMS-0905796 and a Sloan Research Fellowship.
  • An extension of part of the bordered Floer package was used to perform computations for "Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers" is available here.
    • This is version 1 (March 14, 2012).
    • Partial documentation is included.
    • The extension is Copyright 2012 Robert Lipshitz and David Treumann.
    • This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
    • This was supported by NSF Grant DMS-1149800.

Khovanov homology

Sucharit Sarkar and I constructed a stable homotopy refinement of Khovanov homology and gave a formula for computing the induced map Sq2 on Khovanov homology. We also used this to give a refinement of Rasmussen's s-invariant. We (mostly Sucharit) implemented these algorithms in code. These were supported by NSF Grant DMS-1149800.

There is also faster code for doing these kinds of computations, written by others:

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.