- "Bordered Floer homology and the spectral sequence of a branched double cover II: the spectral sequences agree" with Peter
Ozsváth and Dylan Thurston. Journal of Topology, accepted.
- on the arXiv: arXiv:1404.2894.

- "Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers" with David Treumann. Journal of the European Mathematical Society, Vol. 18 (2016), no. 2, 281-325.
- On the arXiv: arXiv:1203.2963.
- Review on MathSciNet (requires subscription).

- "Khovanov homotopy types and the Dold-Thom functor" with Brent Everitt, Sucharit Sarkar and Paul Turner. Homology, Homotopy and Applications, accepted.
- On the arXiv: arXiv:1202.1856.

- "Bordered Floer homology and the branched double cover I" with Peter Ozsváth and Dylan Thurston. Journal of Topology, Vol. 7 (2014), no. 4, 1155-1199.
- On the arXiv: arXiv:1011.0499.
- Review on MathSciNet (requires subscription).

- "Computing HF^ by factoring mapping classes" with Peter Ozsváth and Dylan Thurston. Geometry & Topology, Vol. 18 (2014), no. 5, 2547-2681.
- On the arXiv: arXiv:1010.2550.
- Review on MathSciNet (requires subscription).

- "Bimodules in bordered Heegaard Floer homology" with Peter Ozsváth and Dylan Thurston. Geometry & Topology, Vol. 19 (2015), no. 2, 525-724.
- On the arXiv: arXiv:1003.0598.
- Review on MathSciNet (requires subscription).

- "Notes on bordered Floer homology" with Peter
Ozsváth and Dylan Thurston. In Contact and Symplectic Topology, Bolyai Society Mathematical Studies, Vol. 26 (2014) 275-355.
- On the arXiv: arXiv:1211.6791.
- Review on MathSciNet (requires subscription).

- "On transverse invariants from Khovanov homology" with Lenhard Ng and Sucharit Sarkar. Quantum Topology, Vol. 6 (2015), no. 3, 475-513.
- On the arXiv: arXiv:1303.6371.
- Review on MathSciNet (requires subscription).

- "A Steenrod square on Khovanov homology" with Sucharit Sarkar. Journal of Topology, 7 (2014), no. 3, 817-848.
- On the arXiv: arXiv:1204.5776.
- Review on MathSciNet (requires subscription).

- "A refinement of Rasmussen's
*s*-invariant" with Sucharit Sarkar. Duke Mathematical Journal, Vol. 163 (2014), no. 5, 923-952.- On the arXiv: arXiv:1206.3632.
- Review on MathSciNet (requires subscription).

- "A Khovanov stable homotopy type" with Sucharit Sarkar. Journal of the American Mathematical Society, Vol. 27 (2014), 983-1042.
- On the arXiv: arXiv:1112.3932.
- Review on MathSciNet (requires subscription).
- Former titles: "A Khovanov homotopy type or two"; using an idea of Oleg Viro we can now show the two variants agree. "A Khovanov homotopy type"; the referee suggested adding the word "stable" to avoid confusion.

- "Errata to 'A cylindrical reformulation of Heegaard Floer homology'". Geometry & Topology, Vol. 18 (2014) 17-30.
- on the arXiv: arXiv:1301.4919.
- Review on MathSciNet (requires subscription).
- Further minor corrections and explanations. Last updated December 16, 2015.

- "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, Vol. 15 (2013), no. 4, pp. 1279-1307.
- On the arXiv: arXiv:1012.1032.
- Review on MathSciNet (requires subscription).

- "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 (listed above).
- Further minor corrections and explanations.

- "Bordered Heegaard Floer homology: Invariance and pairing" with Peter Ozsváth and Dylan Thurston.
- On the arXiv: math/0810.0687.
- Last updated: April 25, 2014.

- "Relative Q-gradings from bordered Floer theory" with Peter
Ozsváth and Dylan Thurston.
- on the arXiv: arXiv:1211.6990.
- Last updated: November 30, 2012.

- "Cornered Heegaard Floer homology" with Christopher Douglas and Ciprian Manolescu.
- on the arXiv: arXiv:1309.0155.
- Last updated: August 31, 2013.

- "Heegaard Floer Homologies: lecture notes."
- On the arXiv: arXiv:1411.4540.
- Last updated: November 17, 2014.

- "Khovanov homotopy type, Burnside category, and products" with Tyler Lawson and Sucharit Sarkar.
- on the arXiv: arXiv:1505.00213.
- Last updated: May 1, 2015.

- "The cube and the Burnside category" with Tyler Lawson and Sucharit Sarkar.
- on the arXiv: arXiv:1505.00512.
- Last updated: May 4, 2015.

- "A flexible construction of equivariant Floer homology and applications" with Kristen Hendricks and Sucharit Sarkar.
- on the arXiv: arXiv:1510.02449.
- Last updated: October 8, 2015.

Papers written by undergraduate students I have advised are here.

- 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 Sq
^{1}and Sq^{2}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 Sq
^{2}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.