Selected Papers

List of all papers

  1. Transfinite Milnor invariants for 3-manifolds (with Kent E. Orr)
    • Preprint arxiv:2002.03208 (54 pages)
  2. Primary decomposition in the smooth concordance group of topologically slice knots
    • Preprint arxiv:1910.14629 (35 pages)
  3. Two-solvable and two-bipolar knots with large four-genera (with Allison N. Miller and Mark Powell)
    Mathematical Research Letters, to appear
    • Preprint arxiv:1901.02060 (31 pages)
  4. A family of freely slice good boundary links (with Min Hoon Kim and Mark Powell)
    Mathematische Annalen 376 (2020), 1009–1030.
    • Published • Preprint arxiv:1807.05474
  5. The bipolar filtration of topologically slice knots (with Min Hoon Kim)
    Preprint arxiv:1710.07803 (23 pages) 
  6. Unknotted gropes, Whitney towers, and doubly slicing knots (with Taehee Kim)
    Transactions of the American Mathematical Society 371 (2019), 2383–2429.
    Published • Preprint arXiv:1612.02226
  7. Rational Whitney tower filtration of links
    Mathematische Annalen 370 (2018), no. 3, 963–992.
    • Published • Preprint arXiv:1609.05161
  8. Whitney towers and abelian invariants of knots (with Mark Powell and Kent E. Orr)
    Mathematische Zeitschrift 294 (2020), 519–553.
    Published • Preprint arXiv:1606.03608 
  9. 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.
    Published  Preprint arXiv:1512.08931
  10. The Grothendieck group of polytopes and norms (with Stefan Friedl and Florian Funke)
    Münster Journal of Mathematics 10 (2017), 75–81.
    Published • Preprint arXiv:1512.06699
  11. Complexities of 3-manifolds from triangulations, Heegaard splittings, and surgery presentations
    Quarterly Journal of Mathematics 69 (2018) no. 2, 425–442.
    Published • Preprint arXiv:1506.00757
  12. Complexity of surgery manifolds and Cheeger-Gromov invariants
    International Mathematics Research Notices (IMRN) 2016, no. 18, 5603–5615.
    Published • Preprint arXiv:1506.00758
  13. 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.
    • Published
  14. 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)
  15. Casson towers and slice links (with Mark Powell)
    Inventiones Mathematicae 205 (2016), no.2, 413–457.
    • Published • Preprint arXiv:1411.1621
  16. 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.
    • Published  Preprint arXiv:1405.1805
  17. Non-concordant links with homology cobordant zero framed surgery manifolds (with Mark Powell)
    Pacific Journal of Mathematics 272 (2014), no. 1, 1–33.
    • Published • Preprint arXiv:1309.5051
  18. Splitting numbers of links (with Stefan Friedl and Mark Powell)
    Proceedings of the Edinburgh Mathematical Society 60 (2017) no. 3, 587–614.
    • Published • Preprint arXiv:1308.5638
  19. Covering link calculus and the bipolar filtration of topologically slice links (with Mark Powell)
    Geometry and Topology 18 (2014), no. 3, 1539–1579.
    • Published • Preprint arXiv:1212.5011
  20. 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.
    • PublishedPreprint arXiv:1212.2924
  21. Symmetric Whitney tower cobordism for bordered 3-manifolds and links
    Transactions of the American Mathematical Society 366 (2014), no. 6, 3241–3273.
    • Published • Preprint arXiv:1204.4968
  22. Concordance to links with unknotted components (with Daniel Ruberman)
    Algebraic and Geometric Topology 12 (2012), 963–977.
    • Published • Preprint arXiv:1103.2417
  23. Hidden torsion, 3-manifolds, and homology cobordism (with Kent E. Orr)
    Journal of Topology 6 (2013), no. 2, 490–512.
    PublishedPreprint arXiv:1101.4092
  24. 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.
    PublishedPreprint arXiv:1012.2045
  25. Amenable $L^2$-theoretic methods and knot concordance
    International Mathematics Research Notices (IMRN) 2014, no. 17, 4768–4803.
    PublishedPreprint arXiv:1010.1058
  26. Twisted torsion invariants and link concordance (with Stefan Friedl)
    Forum Mathematicum 25 (2013), no. 3, 471–504.
    Published • Preprint arXiv:1001.0926
  27. $L^2$-signatures, homology localization, and amenable groups (with Kent E. Orr)
    Communications on Pure and Applied Mathematics 65 (2012), no. 6, 790–832.
    Published • Preprint arXiv:0910.3700
  28. The cobordism group of homology cylinders (with Stefan Friedl and Taehee Kim)
    Compositio Mathematica 147 (2011), 914–942.
    Published • Preprint arXiv:0909.5580
  29. 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.
    Published • Preprint arXiv:0705.0088
  30. Structure of the string link concordance group and Hirzebruch-type invariants
    Indiana University Mathematics Journal 58 (2009), 891–928.
    Published • Preprint arXiv:0709.2968
  31. Covering link calculus and iterated Bing doubles (with Taehee Kim)
    Geometry and Topology 12 (2008), 2173–2201.
    PublishedPreprint arXiv:0712.3762
  32. Topological minimal genus and $L^2$-signatures
    Algebraic and Geometric Topology 8 (2008), 885–909.
    PublishedPreprint arXiv:math.GT/0609411
  33. 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.
    PublishedPreprint arXiv:math.GT/0612419
  34. Injectivity theorems and algebraic closures with coefficients
    Proceedings of the London Mathematical Society 96 (2008), no. 1, 227–250.
    Published • Preprint arXiv:math/0609409
  35. The structure of the rational concordance group of knots
    Memoirs of the American Mathematical Society 189 (2007), no. 885, x+95pp.
    Published • Google Books • Preprint arXiv:math/0609408
  36. Signature invariants of covering links (with Ki Hyoung Ko)
    Transactions of the American Mathematical Society 358 (2006), 3399–3412.
    Published Preprint arXiv:math.GT/0108206
  37. 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.
    PublishedPreprint arXiv:math.GT/0109134
  38. Knot signature functions are independent (with Charles Livingston)
    Proceedings of the American Mathematical Society 132 (2004), 2809–2816.
    PublishedPreprint arXiv:math.GT/0208225
  39. Fibred knots and twisted Alexander invariants
    Transactions of the American Mathematical Society 355 (2003), 4187–4200.
    PublishedPreprint arXiv:math.GT/0109136
  40. Signatures of links in rational homology spheres (with Ki Hyoung Ko)
    Topology 41 (2002), 1161–1182.
    PublishedPreprint arXiv:math.GT/0108197
  41. On equivariant slice knots (with Ki Hyoung Ko)
    Proceedings of the American Mathematical Society (1999) 127, no. 7, 2175–2182.
  42. 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.
  43. 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.
  44. 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.