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:
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Correction terms of double branched covers and symmetries of immersed curves
w/ Marco Marengon, Biji Wong. [arXiv version] |
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Satellite knots and immersed Heegaard Floer homology
w/ Wenzhao Chen. [arXiv version] |
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Knot Floer homology as immersed curves
[arXiv version] |
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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] |
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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] |
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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] |
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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] |
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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] |
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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] |
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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] |
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Splicing integer framed knot complements and bordered Heegaard Floer homology
Quantum Topol. 8 (2017), no. 4, 715–748. [arXiv version] |
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Bordered Heegaard Floer homology and graph manifolds
Algebr. Geom. Topol. 16 (2016), no. 6, 3103–3166. [arXiv version] |
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