Publications

• "A faithful linear-categorical action of the mapping class group of a surface with boundary" with Peter Ozsváth and Dylan Thurston. Journal of the European Mathematical Society, accepted.
  • on the arXiv: arXiv:1012.1032.
• "Heegaard Floer homology as morphism spaces" with Peter Ozsváth and Dylan Thurston. Quantum Topology, Vol. 2 (2011), no. 4, pp. 381-449.
  • On the arXiv: arXiv:1005.1248.
  • Review on MathSciNet (requires subscription).
• "A tour of bordered Floer theory" with Peter Ozsváth and Dylan Thurston. Proceedings of the National Academy of Science, Vol. 108, no. 20, pp. 8085-8092. May 17, 2011.
  • On the arXiv: math/1107.5621.
  • Review on MathSciNet (requires subscription).
• "Slicing planar grid diagrams: a gentle introduction to bordered Heegaard Floer homology" with Peter Ozsváth and Dylan Thurston. Proceedings of 15th Gökova Geometry-Topology Conference, 91-119.
  • On the arXiv: math/0810.0695.
  • Review on MathSciNet (requires subscription).
• "Heegaard Floer homology, double points and nice diagrams." Proceedings of the Conference "New Perspectives and Challenges in Symplectic Field Theory, Stanford, June 2007." CRM Proceedings & Lecture Notes, Vol. 49 (2009), 327–342.
  • This paper in PDF format.
  • Review on MathSciNet (requires subscription).
• "Combinatorial cobordism maps in hat Heegaard Floer theory" with Ciprian Manolescu and Jiajun Wang. Duke Math. J., Vol. 145 (2008), no 2., pp. 207-247.
  • On the arXiv: math/0611927.
  • Review on MathSciNet (requires subscription).
• "Covering spaces and Q-gradings on Heegaard Floer homology" with Dan Lee. J. Symplectic Geom., Vol. 6 (2008), no. 1, 33-59.
  • On the arXiv: math/0608001. An updated version is available here.
  • Review on MathSciNet (requires subscription)
• "A Heegaard-Floer invariant of bordered 3-manifolds." Ph.D. thesis, Stanford University, 2006.
  • This paper in PDF format.
  • This paper in Postscript format.
  • Also available from ProQuest dissertation database (requires subscription)
• "A cylindrical reformulation of Heegaard Floer homology". Geom. Topol. 10 (2006), pp. 955-1097.
  • on the arXiv: math/0502494.
  • Review on MathSciNet (requires subscription).
  • Errata.

Preprints (not yet accepted for publication)

• "Bordered Heegaard Floer homology: Invariance and pairing" with Peter Ozsváth and Dylan Thurston.
  • On the arXiv: math/0810.0687.
  • Last updated: June 1, 2011.
• "Bimodules in bordered Heegaard Floer homology" with Peter Ozsváth and Dylan Thurston.
  • On the arXiv: arXiv:1003.0598.
  • Last updated: June 29, 2011.
• "Computing HF^ by factoring mapping classes" with Peter Ozsváth and Dylan Thurston.
  • on the arXiv: arXiv:1010.2550.
  • Last updated: June 29, 2011.
• "Bordered Floer homology and the branched double cover I" with Peter Ozsváth and Dylan Thurston.
  • on the arXiv: arXiv:1011.0499.
  • Last updated: November 2, 2010.
• "A Khovanov homotopy type" with Sucharit Sarkar.
  • on the arXiv: arXiv:1112.3932.
  • Last updated: August 8, 2012.
  • Former title: "A Khovanov homotopy type or two"; using an idea of Oleg Viro we can now show the two variants agree.
• "Khovanov homotopy types and the Dold-Thom functor" with Brent Everitt, Sucharit Sarkar and Paul Turner.
  • on the arXiv: arXiv:1202.1856.
  • Last updated: February 8, 2012.
• "Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers" with David Treumann.
  • on the arXiv: arXiv:1203.2963.
  • Last updated: September 9, 2012.
• "A Steenrod square on Khovanov homology" with Sucharit Sarkar.
  • on the arXiv: arXiv:1204.5776.
  • Last updated: April 25, 2012.
• "A refinement of Rasmussen's s-invariant" with Sucharit Sarkar.
  • on the arXiv: arXiv:1206.3632.
  • Last updated: June 15, 2012.
• "Notes on bordered Floer homology" with Peter Ozsváth and Dylan Thurston.
  • on the arXiv: arXiv:1211.6791.
  • Last updated: November 30, 2012.
• "Relative Q-gradings from bordered Floer theory" with Peter Ozsváth and Dylan Thurston.
  • on the arXiv: arXiv:1211.6990.
  • Last updated: November 30, 2012.
• "Errata to 'A cylindrical reformulation of Heegaard Floer homology'"
  • on the arXiv: arXiv:1301.4919.
  • Last updated: January 21, 2013.
• "On transverse invariants from Khovanov homology" with Lenhard Ng and Sucharit Sarkar.
  • on the arXiv: arXiv:1303.6371.
  • Last updated: March 26, 2013.

Papers written by undergraduate students I have advised are here.

Programming

• A technology demonstration (i.e., far pre-beta version) of a package to compute Heegaard Floer invariants using bordered Floer homology is here.
  • You will need Sage to run it.
  • This is version 0.2 (August 5, 2011), the second release on the web. 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).
  • Bohua Zhan has ported this program to C++. The port is much faster. Send him e-mail if you are interested in it.
  • Bohua Zhan also has a Sage rewrite and extension of the code, available on GitHub.
  • Partial documentation is included, in a PDF called BordProgDocs
  • Please e-mail me if you find bugs. (I'm sure they're there.) Programming style criticism also accepted.
  • 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.
• 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".
  • The extension is available here.
  • This is version 1 (March 14, 2012).
  • Like the paper, this extension is joint work with David Treumann.
  • 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.
• Code for computing the actions of Sq¹ and Sq² on Khovanov homology, written mainly by Sucharit Sarkar. Used in and based on our paper "A Steenrod square on Khovanov homology".
• Code for computing the refined s-invariant from Sq² on Khovanov homology, written mainly by Sucharit Sarkar. Used in and based on our paper "A refinement of Rasmussen's s-invariant".

Some programs by other Columbia-affiliated topologists are here. CompuTop has a more extensive list of programs for doing computations in low-dimensional topology.