Symmetric chain complexes, twisted Blanchfield pairings, and knot concordance, with Allison N. Miller. Preprint. Here is a Maple program that implements our algorithm.
Triple linking numbers and surface systems, with Christopher W. Davis, Matthias Nagel and Patrick Orson. Preprint.
Smooth and topological almost concordance, with Matthias Nagel, Patrick Orson and Jung Hwan Park. Preprint.
The round handle problem, with Min Hoon Kim and Peter Teichner. Preprint.
Whitney towers and abelian invariants of knots, with Jae Choon Cha and Kent E. Orr. Preprint.
Satellites and concordance of knots in 3-manifolds, with Stefan Friedl, Matthias Nagel and Patrick Orson. To appear in Transactions of the AMS.
Twisted Blanchfield pairings and decompositions of 3-manifolds, with Stefan Friedl, Constance Leidy and Matthias Nagel. Homology, homotopy and applications 19, Issue 2 (2017) 275–287.
Stable classification of 4-manifolds with 3-manifold fundamental groups, with Daniel Kasprowski, Markus Land and Peter Teichner. Journal of Topology 10 (2017) 827-881.
Splitting numbers of links, with Jae Choon Cha and Stefan Friedl. Proceedings of the Edinburgh Mathematical Society Volume 60, Issue 3 (2017), 587-614.
Grope metrics on the knot concordance set, with Tim D. Cochran and Shelly Harvey. Journal of Topology 10 (2017) 669-699.
A calculation of Blanchfield pairings of 3-manifolds and knots, with Stefan Friedl. Moscow Mathematical Journal, Volume 17 (2017), Issue 1, 59-77.
The four genus of a link, Levine-Tristram signatures and satellites. Journal of Knot Theory and its Ramifications, special memorial edition in honour of Tim Cochran, Vol. 26, No. 2, (2017).
Concordance invariance of Levine-Tristram signatures of links, with Matthias Nagel. Documenta Mathematica 22 (2017), 25-43.
Twisted Blanchfield pairings and symmetric chain complexes. Quarterly Journal of Mathematics, Volume 67 (2016), Issue 4, 715-742.
Casson towers and slice links, with Jae Choon Cha. Inventiones Mathematicae 205 (2016), Issue 2, 413-457.
Blanchfield forms and Gordian distance, with Maciej Borodzik and Stefan Friedl. Minor revision from the version that appeared in Journal of the Mathematical Society of Japan 68 (2016), no. 3, 1047 - 1080.
Embedded Morse theory and relative splitting of cobordisms of manifolds, with Maciej Borodzik. Journal of Geometric Analysis 26 (2016), no. 1, 57-87.
A specious unlinking strategy, with Stefan Friedl and Matthias Nagel. Periodica Mathematica Hungarica 69 (2014), no. 2, 207-210.
Shrinking of toroidal decomposition spaces, with Daniel Kasprowski. Fundamenta Math. 227 (2014), 271-296.
Non-concordant links with homology cobordant zero framed surgery manifolds, with Jae Choon Cha. Pacific Journal of Mathematics 272-1 (2014), 1-33.
Covering link calculus and the bipolar filtration of topologically slice links, with Jae Choon Cha. Geometry & Topology 18 (2014), 1539–1579.
Concordance of links with identical Alexander invariants, with Jae Choon Cha and Stefan Friedl. Bull. London Math. Soc. 46 (2014), No. 3, pp. 629-642.
Links not concordant to the Hopf link; with Stefan Friedl. Math. Proc. Camb. Phil. Soc. 156 (2014), 425-459.
Cobordisms to weakly splittable links, with Stefan Friedl. Proc. Amer. Math. Soc. 142 (2014), 703-712.
Cosmetic crossings and Seifert Matrices; with Cheryl Balm, Stefan Friedl and Effie Kalfagianni. Communications in Analysis and Geometry 20 (2012), 235-253.
An Injectivity Theorem for Casson-Gordon Type Representations relating to Knot and Link Concordance, with Stefan Friedl. Bulletins of the KMS 49 (2012), No. 2, 395-409.
A second order algebraic knot concordance group, a shorter version of my thesis. Algebraic & Geometric Topology 12 (2012) 685-751.
Smoothly slice boundary links whose derivative links have nonvanishing Milnor invariants,
with Hye Jin Jang and Min Hoon Kim. Michigan Math. Journal 63 (2014), No. 2, pp. 423-446.
The proof that our links are smoothly slice contains what seems to be a serious mistake: the embedding Y x I does not exist as claimed on pages 16 and 17.
My PhD thesis on a second order algebraic knot concordance group.