Lukas Lewark
Publications and Preprints

Here are links for my papers on the arXiv, on MathSciNet, and on zbMATH.

Here are links for my reviews for zbMATH and for MathSciNet.

My co-authors: Sebastian Baader, Ian Banfield, Peter Feller, Stefan Friedl, Eugene Gorsky, Damian Iltgen, Marc Kegel, Takahiro Kitayama, Alexandra Kjuchukova, Livio Liechti, Andrew Lobb, Naageswaran Manikandan, Laura Marino, Duncan McCoy, Filip Misev, Léo Mousseau, Matthias Nagel, Mark Powell, Arunima Ray, Marithania Silvero, Paula Truöl, Raphael Zentner, Claudius Zibrowius.

List of my papers in reverse chronological order of appearance on the arXiv:

26. The second coefficient of the Alexander polynomial as a satellite obstruction
arXiv:2402.03155 pdf
25. A new concordance homomorphism from Khovanov homology
arXiv:2401.08480 pdf
24. On unknotting fibered positive knots and braids
joint with Marc Kegel, Naageswaran Manikandan, Filip Misev, Léo Mousseau and Marithania Silvero.
arXiv:2312.07339 pdf
23. 3-braid knots with maximal 4-genus
joint with Sebastian Baader, Filip Misev and Paula Truöl.
Transactions of the American Mathematical Society Series B 11 (2024), 600–621.
arXiv:2303.11918 pdf
22. Rasmussen invariants of Whitehead doubles and other satellites
joint with Claudius Zibrowius
arXiv:2208.13612 pdf
Videos of talks about this paper: video Oaxaca.
21. Quasipositivity and braid index of pretzel knots
Communications in Analysis and Geometry (accepted for publication).
arXiv:2205.05347 pdf
20. On the values taken by slice torus invariants
joint with Peter Feller and Andrew Lobb
Mathematical Proceedings of the Cambridge Philosophical Society 176 (2024), no. 1, pp. 55–63.
arXiv:2202.13818 pdf
19. Squeezed Knots
joint with Peter Feller and Andrew Lobb
Quantum Topology (accepted for publication)
arXiv:2202.12289 pdf
Videos of talks about this paper: video CIRGET, video Lipshitz & Sarkar @ ICM 2018.
18. Khovanov homology and rational unknotting
joint with Damian Iltgen and Laura Marino
arXiv:2110.15107 pdf
Videos of talks about this paper: video Georgia.
17. Rasmussen invariants
joint with Claudius Zibrowius
published in June 2021. Not on the arXiv.
Mathematical Research Postcards, vol. 1 no. 2 pdf
16. Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials
joint with Stefan Friedl, Takahiro Kitayama, Matthias Nagel and Mark Powell
Canadian Journal of Mathematics 74 (2022), no. 4, pp. 1137–1176.
arXiv:2007.15289 pdf
15. Untwisting 3-strand torus knots
joint with Sebastian Baader and Ian Banfield
Bulletin of the London Mathematical Society 52 (2020), no. 3, pp. 429–436.
arXiv:1909.01003 pdf, MR4171377
14. Balanced algebraic unknotting, linking forms, and surfaces in three- and four-space
joint with Peter Feller
Journal of Differential Geometry (accepted for publication)
arXiv:1905.08305 pdf
Videos of talks about this paper: video K-OS.
13. Average four-genus of two-bridge knots
joint with Sebastian Baader, Alexandra Kjuchukova, Filip Misev and Arunima Ray
Proceedings of the AMS (accepted for publication)
arXiv:1902.05721 pdf
12. Almost positive links are strongly quasipositive
joint with Peter Feller and Andrew Lobb
Mathematische Annalen 385 (2023), pp. 481–510.
arXiv:1809.06692 pdf
11. Upsilon-like concordance invariants from sl(n) knot cohomology
joint with Andrew Lobb
Geometry & Topology 23 (2019), no. 2, pp. 745–780
arXiv:1707.00891 pdf, MR3939052
Videos of talks about this paper: video Cambridge.
10.Checkerboard graph monodromies
joint with Sebastian Baader and Livio Liechti
L'Enseignement Mathématique 64 (2018), no. 2, pp. 65–88
arXiv:1706.09210 pdf, MR3959848
9.On calculating the slice genera of 11- and 12-crossing knots
joint with Duncan McCoy
Experimental Mathematics 28 (2019), no. 1, pp. 81–94
arXiv:1508.01098v2 pdf, MR3938580
8.On classical upper bounds for slice genera
joint with Peter Feller
Selecta Mathematica 24 (2018), no. 5, pp. 4885–4916
arXiv:1611.02679 pdf, MR3874707
Videos of talks about this paper: video Cambridge, video Banff.
7.Khovanov width and dealternation number of positive braid links
joint with Sebastian Baader, Peter Feller and Raphael Zentner
Mathematical Research Letters 26 (2019), no. 3, pp. 627–641
arXiv:1610.04534 pdf, MR4028096
6.On the topological 4-genus of torus knots
joint with Sebastian Baader, Peter Feller and Livio Liechti
Transactions of the AMS 370 (2018), pp. 2639–2656
arXiv:1509.07634 pdf, MR3748580
5.The stable 4-genus of alternating knots
joint with Sebastian Baader
Asian Journal of Mathematics 21 (2017), no. 6, pp. 1183–1190
arXiv:1505.03345 pdf, MR3778124
4.New Quantum Obstructions to Sliceness
joint with Andrew Lobb
Proceedings of the LMS 112 (2016), no. 1, pp. 81–114
arXiv:1501.07138 pdf, MR3458146
3.On stable sl3-homology of torus knots
joint with Eugene Gorsky
Experimental Mathematics 24 (2015), no. 2, pp. 162–174
arXiv:1404.0623 pdf, MR3350523
2.Rasmussen's spectral sequences and the sl(N)-concordance invariants
Advances in Mathematics 260C (2014), pp. 59–83
arXiv:1310.3100 pdf, MR3209349
1.sl3-foam homology calculations
Algebraic & Geometric Topology 13 (2013), no. 6, 3661–3686
arXiv:1212.2553 pdf, MR3248745
Last update: 22 April 2024.