Preprints:
Lagrangian Zigzag Cobordisms
Joint with Joshua Sabloff, C.-M. Mike Wong and Angela Wu
Submitted, 2024
arXiv: 2308.02057 [math.SG]
Transverse braids and combinatorial knot Floer homology
Joint with Peter Lambert-Cole:
Submitted, 2017
arXiv: 1703.06861 [math.SG]
Braids and combinatorial knot Floer homology
Joint with Peter Lambert-Cole and Michaela Stone:
Under revision at Mathematical Research Letters, 2016
arXiv: 1312.5586 [math.GT]
Publications:
Upper bounds for the Lagrangian cobordism relation on Legendrian links
Joint with Joshua Sabloff and C.-M. Mike Wong
Algebraic & Geometric Topology, 24-8 (2024), 4237–4263.
doi: 10.2140/agt.2024.24.4237; arXiv: 2105.02390 [math.SG]
Ribbon homology cobordisms
Joint with Aliakbar Daemi, Tye Lidman and C.-M. Mike Wong.
Advances in Mathematics, 408 (2022), 108580, 68 Pages (journal link)
MR: 4467148; doi: 10.1016/j.aim.2022.108580; arXiv: 1904.09721 [math.GT]
Lifting Lagrangian immersions in CP^(n-1) to Lagrangian cones in C^n
Joint with Scott Baldridge and Ben McCarty.
Open Book Series, 5 (2022), No. 1, 43–79 (journal link)
doi: 10.2140/obs.2022.5.43; arXiv: 1708.09048 [math.GT]
An unoriented skein relation via bordered–sutured Floer homology
Joint with C.-M. Mike Wong.
Journal of Symplectic Geometry 19 (2021), no. 6, 1495-1561 (journal link)
MR: 4450627; doi: 10.4310/JSG.2021.v19.n6.a4 ; arXiv: 1811.00134 [math.GT]
A note on the knot Floer homology of fibered knots
Joint with John A. Baldwin.
Algebraic & Geometric Topology 18 (2018), no. 6, 3669–3690 (journal link)
MR: 3868231; doi: 10.2140/agt.2018.18.3669; arXiv: 1801.06563 [Math.GT]
Sutured Floer homology and invariants of Legendrian and transverse knots
Joint with John B. Etnyre and Rumen Zarev:
Geometry & Topology 21 (2017), no. 2, 1469-1582 (journal link)
MR: 3650078; Zbl: 06726508; doi: 10.2140/gt.2017.21.1469; arXiv: 1408.5858 [math.GT]
Generalized Gauss Maps and Integrals for Three-Component Links: Toward Higher Helicities for Magnetic Fields and Fluid Flows, Part 2
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Haggai Nuchi and Clayton Shonkwiler:
Algebraic & Geometric Topology 13 (2013), no. 5, 2897-2923 (journal link)
MR: 3116307; Zbl: 06198033; doi: 10.2140/agt.2013.13.2897; arXiv: 1207.1793 [math.GT]
On the Equivalence of Legendrian and Transverse Invariants in Knot Floer Homology
Joint with John A. Baldwin and Vera Vértesi:
Geometry & Topology 17 (2013), no. 2, 925-974 (journal link)
MR: 3070518; Zbl: 1285.57005; doi: 10.2140/gt.2013.17.925; arXiv: 1112.5970 [math.SG]
Generalized Gauss Maps and Integrals for Three-Component Links: Toward Higher Helicities for Magnetic Fields and Fluid Flows
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin and Clayton Shonkwiler:
Journal of Mathematical Physics 54 013515 (2013) (journal link)
MR: 3059903; Zbl: 06255553; doi: 10.1063/1.4774172; arXiv: 1101.3374 [math.GT]
On the Transverse Invariant for Bindings of Open Books
Journal of Differential Geometry 88 (2011), no. 3, 533-552
MR: 2844442; Zbl: 06011497; arXiv: 0806.1729 [math.SG]
–
Legendrian Contact Homology and Nondestabilizability
Joint with Clayton Shonkwiler:
Journal of Symplectic Geometry 9 (2011), no. 1, 33-44 (journal link)
MR: 2787360; Zbl: 1226.57013; doi: 10.4310/JSG.2011.v9.n1.a3; arXiv: 0910.3914 [math.GT]
Higher-Dimensional Linking Integrals
Joint with Clayton Shonkwiler:
Proceedings of the American Mathematical Society 139 (2011), no. 4, 1511-1519 (journal link)
MR: 2748445; Zbl: 1221.57038; doi: 10.1090/S0002–9939–2010–10603–2; arXiv: 0801.4022 [math.GT]
Torsion and Open Book Decompositions
Joint with John B. Etnyre:
International Mathematics Research Notices (2010), no. 22, 4385-4398
MR: 2737776; Zbl: 1213.57028; doi: 10.1093.imrn.rnq054; arXiv: 0909.3465 [math.SG].
Triple Linking Numbers, Hopf Invariants and Integral Formulas for Three-Component Links
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin and Clayton Shonkwiler:
Matemátcia Contemporânea 34 (2008), 251-283 (journal link)
Special volume in honor of Manfredo P. do Carmo’s 80th birthday.
MR: 2588614; Zbl: 1194.57007; arXiv: 0901.1612 [math.GT]
The Four Vertex Theorem and its Converse
Joint with Dennis DeTurck, Herman Gluck and Daniel Pomerleano:
Notices of the American Mathematical Society 54 (2007), no. 2, 192-207 (journal link)
MR: 2285124; arXiv: 0609268 [math.DG]
In Preparation:
- Cyclic branched covers and combinatorial invariants of transverse knots
Joint with C.-M. Mike Wong. - The Geometry of Triple Linking: A Survey
Joint with Dennis DeTurck, Herman Gluck, Rafal Komendarczyk, Paul Melvin, Haggai Nuchi and Clayton Shonkwiler.
