Robert Lipshitz



  • "Diagonals and A-infinity Tensor Products" with Peter Ozsváth and Dylan Thurston. arXiv:2009.05222. Last updated September 20, 2021.
  • "A bordered HF- algebra for the torus" with Peter Ozsváth and Dylan Thurston. arXiv:2108.12488. Last updated August 27, 2021.
  • "Khovanov homology of strongly invertible knots and their quotients" with Sucharit Sarkar. arXiv:2203.13895. Last updated March 25, 2022.
  • "Bordered HF- for three-manifolds with torus boundary" with Peter Ozsváth and Dylan Thurston. arXiv:2305.07754. Last updated May 12, 2023.
  • "Floer homology beyond borders" with Peter Ozsváth and Dylan Thurston. arXiv:2307.16330. Last updated July 30, 2023.
  • "Torsion in linearized contact homology for Legendrian knots" with Lenhard Ng. arXiv:2308.13482. Last updated August 25, 2023.
  • "Local equivalence and refinements of Rasmussen's s-invariant" with Nathan Dunfield and Dirk Schütz. arXiv:2312.09114. Last updated December 14, 2023.

Accepted or published

Roughly, my work so far falls into four categories: bordered Heegaard Floer homology, an extension of Heegaard Floer homology to 3-manifolds with boundary; equivariant Lagrangian intersection Floer homology and its applications to Heegaard Floer homology and symplectic Khovanov homology; other topics in Heegaard Floer homology; and Khovanov homology and its stable homotopy refinement. (There is some overlap.) Papers in each category are in approximately the order they were written. A link to each paper on the arXiv and its review on MathSciNet is at the end of each entry. I have not read any of these reviews.

Bordered Heegaard Floer homology


"A faithful linear-categorical action of the mapping class group of a surface with boundary," above, is also partly expository.

Equivariant Floer homology

See also "Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers", above.

Other topics in Heegaard Floer homology


Khovanov homology and homotopy



My research has been supported by a National Science Foundation (NSF) Graduate Research Fellowship, an NSF Mathematical Sciences Postdoctoral Research Fellowship, a Sloan Research Fellowship, and NSF Grants DMS-0905796, DMS-1149800, DMS-1560783, DMS-1642067, and DMS-1810893. The support specific to each paper is listed in that paper.

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.