Jonathan Hanselman




I am interested in low-dimensional topology, in particular the topology of 3-manifolds and knots. I primarily study these objects using Heegaard Floer homology and other techniques related to symplectic geometry. I am especially interested in questions concerning decomposing manifolds or knots through cutting and gluing procedures.

Papers and preprints:


Satellite knots and immersed Heegaard Floer homology
w/ Wenzhao Chen.
[arXiv version]

Knot Floer homology as immersed curves
[arXiv version]

Cabling in terms of immersed curves
w/ Liam Watson.
Geom. Topol. 27-3 (2023), 925-952; DOI 10.2140/gt.2023.27.925
[arXiv version]

Heegaard Floer homology and cosmetic surgeries in S^3
J. Eur. Math. Soc. 25 (2023), no. 5, pp. 1627–1670. DOI 10.4171/JEMS/1218
[arXiv version]

Bordered Floer homology for manifolds with torus boundary: properties and applications
w/ Jacob Rasmussen and Liam Watson.
Proc. Lond. Math Soc. (3) 2022;1-89. DOI 10.1112/plms.12473
[arXiv version]

Bordered Floer homology for manifolds with torus boundary via immersed curves
w/ Jacob Rasmussen and Liam Watson.
J. Amer. Math. Soc. (published electronically Aug 2023) DOI: https://doi.org/10.1090/jams/1029
[arXiv version]

L-spaces, taut foliations, and graph manifolds
w/ Jacob Rasmussen, Sarah Dean Rasmussen, and Liam Watson.
Compos. Math. 156 (2020), no. 3, 604–612.
[arXiv version]

A calculus for bordered Floer homology
w/ Liam Watson.
Geom. Topol. 27-3 (2023), 823-924; DOI 10.2140/gt.2023.27.823
[arXiv version]

A remark on the geography problem in Heegaard Floer homology
w/ Cagatay Kuluhan and Tye Lidman.
Breadth in contemporary topology, 103–111, Proc. Sympos. Pure Math., 102, Amer. Math. Soc., Providence, RI, 2019.
[arXiv version]

Splicing integer framed knot complements and bordered Heegaard Floer homology
Quantum Topol. 8 (2017), no. 4, 715–748.
[arXiv version]

Bordered Heegaard Floer homology and graph manifolds
Algebr. Geom. Topol. 16 (2016), no. 6, 3103–3166.
[arXiv version]



Videos/slides from selected talks:


(video) Knot Floer homology as immersed curves
Talk given (online) at the virtual workshop "Interactions of gauge theory with contact and symplectic topology in dimensions 3 and 4" at BIRS
Online, June 2020

(video) Bordered Floer homology via immersed curves: properties and applications
Talk given at the workshop "Thirty Years of Floer Theory for 3-manifolds" at Casa Matematica Oaxaca
Oaxaca, Mexico, Aug 2017

(slides) Bordered Floer homology for manifolds with torus boundary via immersed curves
AMS Sectional Meeting, UGa, Mar 2016