## Publications

### List of all papers

1. Two-solvable and two-bipolar knots with large four-genera (with Allison N. Miller and Mark Powell)
• Preprint arxiv:1901.02060 (31 pages)
2. A family of freely slice good boundary links (with Min Hoon Kim and Mark Powell)
Mathematische Annalen, to appear.
3. The bipolar filtration of topologically slice knots (with Min Hoon Kim)
Preprint arxiv:1710.07803 (23 pages)
4. Unknotted gropes, Whitney towers, and doubly slicing knots (with Taehee Kim)
Transactions of the American Mathematical Society 371 (2019), 2383–2429.
5. Rational Whitney tower filtration of links
Mathematische Annalen 370 (2018), no. 3, 963–992.
6. Whitney towers and abelian invariants of knots (with Mark Powell and Kent E. Orr)
Mathematische Zeitschrift, to appear.
Published • Preprint arXiv:1606.03608 (34 pages)
7. Rasmussen $s$-invariants of satellites do not detect slice knots (with Min Hoon Kim)
Journal of Knot Theory and Its Ramifications 26 (2017), no. 2, Special issue for Tim Cochran, 1740001.
Preprint arXiv:1512.08931
8. The Grothendieck group of polytopes and norms (with Stefan Friedl and Florian Funke)
Münster Journal of Mathematics 10 (2017), 75–81.
9. Complexities of 3-manifolds from triangulations, Heegaard splittings, and surgery presentations
Quarterly Journal of Mathematics 69 (2018) no. 2, 425–442.
10. Complexity of surgery manifolds and Cheeger-Gromov invariants
International Mathematics Research Notices (IMRN) 2016, no. 18, 5603–5615.
11. Classical homological invariants are not determined by knot Floer homology and Khovanov homology (with Toshifumi Tanaka)
Journal of Knot Theory and Its Ramifications 25 (2016) no. 7, 1650039, 14 pp.
12. Non-meridional epimorphisms of knot groups (with Masaaki Suzuki)
Algebraic and Geometric Topology 16 (2016) no.2, 1135–1155.
Published • Preprint arXiv:1502.06039 (20 pages)
13. Casson towers and slice links (with Mark Powell)
Inventiones Mathematicae 205 (2016), no.2, 413–457.
14. A topological approach to Cheeger-Gromov universal bounds for von Neumann ρ-invariants
Communications on Pure and Applied Mathematics 69 (2016), no. 6, 1154–1209.
15. Non-concordant links with homology cobordant zero framed surgery manifolds (with Mark Powell)
Pacific Journal of Mathematics 272 (2014), no. 1, 1–33.
16. Splitting numbers of links (with Stefan Friedl and Mark Powell)
Proceedings of the Edinburgh Mathematical Society 60 (2017) no. 3, 587–614.
17. Covering link calculus and the bipolar filtration of topologically slice links (with Mark Powell)
Geometry and Topology 18 (2014), no. 3, 1539–1579.
18. Concordance of links with identical Alexander invariants, (with Stefan Friedl and Mark Powell)
Bulletin of the London Mathematical Society 46 (2014), no. 3, 629–642.
19. Symmetric Whitney tower cobordism for bordered 3-manifolds and links
Transactions of the American Mathematical Society 366 (2014), no. 6, 3241–3273.
20. Concordance to links with unknotted components (with Daniel Ruberman)
Algebraic and Geometric Topology 12 (2012), 963–977.
21. Hidden torsion, 3-manifolds, and homology cobordism (with Kent E. Orr)
Journal of Topology 6 (2013), no. 2, 490–512.
22. Smooth concordance of links topologically concordant to the Hopf link (with Taehee Kim, Daniel Ruberman, and Saso Strle)
Bulletin of the London Mathematical Society 44 (2012), 443–450.
23. Amenable $L^2$-theoretic methods and knot concordance
International Mathematics Research Notices (IMRN) 2014, no. 17, 4768–4803.
24. Twisted torsion invariants and link concordance (with Stefan Friedl)
Forum Mathematicum 25 (2013), no. 3, 471–504.
25. $L^2$-signatures, homology localization, and amenable groups (with Kent E. Orr)
Communications on Pure and Applied Mathematics 65 (2012), no. 6, 790–832.
26. The cobordism group of homology cylinders (with Stefan Friedl and Taehee Kim)
Compositio Mathematica 147 (2011), 914–942.
27. Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers
Journal of the European Mathematical Society (JEMS) 12 (2010), no. 3, 555–610.
28. Structure of the string link concordance group and Hirzebruch-type invariants
Indiana University Mathematics Journal 58 (2009), 891–928.
29. Covering link calculus and iterated Bing doubles (with Taehee Kim)
Geometry and Topology 12 (2008), 2173–2201.
30. Topological minimal genus and $L^2$-signatures
Algebraic and Geometric Topology 8 (2008), 885–909.
31. Algebraic and Heegaard-Floer invariants of knots with slice Bing doubles (with Charles Livingston and Daniel Ruberman)
Mathematical Proceedings of the Cambridge Philosophical Society 144 (2008), 403–410.
32. Injectivity theorems and algebraic closures with coefficients
Proceedings of the London Mathematical Society 96 (2008), no. 1, 227–250.
33. The structure of the rational concordance group of knots
Memoirs of the American Mathematical Society 189 (2007), no. 885, x+95pp.
34. Signature invariants of covering links (with Ki Hyoung Ko)
Transactions of the American Mathematical Society 358 (2006), 3399–3412.
35. The effect of mutation on link concordance, 3-manifolds, and the Milnor invariants
Journal of Knot Theory and Its Ramifications 15 (2006), no. 2, 239–257.
36. Knot signature functions are independent (with Charles Livingston)
Proceedings of the American Mathematical Society 132 (2004), 2809–2816.
37. Fibred knots and twisted Alexander invariants
Transactions of the American Mathematical Society 355 (2003), 4187–4200.
38. Signatures of links in rational homology spheres (with Ki Hyoung Ko)
Topology 41 (2002), 1161–1182.
39. On equivariant slice knots (with Ki Hyoung Ko)
Proceedings of the American Mathematical Society (1999) 127, no. 7, 2175–2182.
40. Signature invariants of links from irregular covers and non-abelian covers (with Ki Hyoung Ko)
Mathematical Proceedings of the Cambridge Philosophical Society (1999) 127, 67–81.
41. An identity-based signature from gap Diffie-Hellman groups (with Jung Hee Cheon)
PKC 2003, Lecture Notes in Computer Science 2567 (2002), pp. 18–30.
42. An efficient implementation of braid groups (with Ki Hyoung Ko, Sang Jin Lee, Jae Woo Han, and Jung Hee Cheon)
Asiacrypt 2001, Lecture Notes in Computer Science 2248 (2001), pp. 157–174.

### Papers unpublished

1. Unknown values in the table of knots (with Charles Livingston)
• arXiv:math.GT/0503125

• This note is regularly updated to provide up-to-date information on unknown values of basic knot invariants, in conjunction with the website KnotInfo.
2. A characterization of the Murasugi polynomial of an equivariant slice knot
• arXiv:math.GT/0404403

• The main result and its proof in this paper will appear in an upcoming new edition of J. Hillman’s book “Algebraic Invariants of Links” (World Scientific).
3. Rasmussen invariants and link concordance (with Taehee Kim)
• In this note we observe that Rasmussen’s argument actually shows the invariance of Lee’s degenerated Khovanov homology, as a filtered vector space, under link concordance.  Later this was rediscovered by John Pardon, “The link concordance invariant from Lee homology” (arXiv:1107.4702).
For citation information, see my papers on Google Scholar.