20. Locally flat simple spheres in CP^2
(With A. Conway)
19. Unknotting nonorientable surfaces
(With A. Conway and M. Powell)
18. Mapping class groups of simply connected 4-manifolds with boundary
(With M. Powell)

Published and accepted papers

17. The foundations of four-manifold theory in the topological category
(With S. Friedl, M. Nagel and M. Powell)
To appear in NYJM Monogr.
16. Simple spines of homotopy 2-spheres are unique
(With M. Powell)
Proc. London Math. Soc. (2024), 128: e12583.
15. A calculus for flow categories
(With A. Lobb and D. Schütz)
Adv. Math. 409 (2022), Paper No. 108665, 58 pp.
14. Null, recursively starlike-equivalent decompositions shrink
(With J. Meier and A. Ray)
Glasg. Math. J. (28 October 2022)
13. Abelian invariants of doubly slice links
(With A. Conway)
Enseign. Math. 68 (2022), no. 3, pp. 243–290
12. The relative Whitney trick and its applications
(With C. W. Davis and J. Park)
Selecta Math. (30 December 2021)
11. Embedding spheres in knot traces
(With P. Feller, A. N. Miller, M. Nagel, M. Powell and A. Ray)
Compos. Math. 157(10):2242–2279, 2021.
Me speaking about this paper at the NCNGT Conference 2020:
10. A lower bound for the doubly slice genus from signatures
(With M. Powell)
New York J. Math. 27 (2021), 379–392.
9. Doubly slice knots and metabelian obstructions
(With M. Powell)
J. Topol. Anal (6 February 2021)
8. Triple linking numbers and surface systems
(With C. W. Davis, M. Nagel and M. Powell)
Indiana Univ. Math. J. 69 (2020), 2505-2547
7. Khovanov homotopy calculations using flow category calculus
(With A. Lobb and D. Schütz)
Exp. Math. (9 April 2019)
6. Smooth and topological almost concordance
(With M. Nagel, J. Park and M. Powell)
Int. Math. Res. Not. (2019), no. 23, 7324–7355.
5. Satellites and concordance of knots in 3-manifolds
(With S. Friedl, M. Nagel and M. Powell)
Trans. Amer. Math. Soc. 371 (2019), 2279-2306
4. Framed cobordism and flow category moves
(With A. Lobb and D. Schütz)
Algebr. Geom. Topol 18 (2018), no. 5, 2821-2858
3. A Khovanov stable homotopy type for colored links
(With A. Lobb and D. Schütz)
Algebr. Geom. Topol. 17 (2017), no. 2, 1261-1281
2. Double L-groups and doubly-slice knots
Algebr. Geom. Topol. 17 (2017), no. 1, 273-329
1. Twist spinning of knots and metabolizers of Blanchfield pairings
(With S. Friedl)
Annales de Toulouse, Série 6, Volume 24, Fascicule 5 (2015)

Textbook chapters

Author on the following chapters of the Oxford University Press textbook
The disc embedding theorem, edited by S. Behrens, B. Kalmár, M. H. Kim, M. Powell, and A. Ray.

  • The Whitehead decomposition (with X. Cui, B. Kalmár, and N. Sunukjian)
  • Shrinking starlike sets (with J. Meier, and A. Ray)
  • Good groups (with M. H. Kim, J. Park, and A. Ray)
  • The s-cobordism theorem, the sphere embedding theorem and the Poincaré conjecture (with M. Powell, and A. Ray.)
  • Surgery theory and the classification of closed, simply connected 4-manifolds (with M. Powell, and A. Ray)
  • Open problems (with M. H. Kim, J. Park, and A. Ray)

Unpublished notes

Double Witt groups
(Will remain permanently a preprint as, after uploading this to the arXiv, I was informed that the main result can be obtained already as a consequence of work by Quebbeman-Scharlau-Schulte.)