Submitted preprints
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22. Smoothing topological pseudo-isotopies of 4-manifolds
With M. Powell and O. Randal-Williams |
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21. Simply slicing knots
With A. Conway and M. Pencovitch |
Published papers
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20. Unknotting nonorientable surfaces
With A. Conway and M. Powell J. Eur. Math. Soc. (2025) |
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19. Mapping class groups of simply connected 4-manifolds with boundary
With M. Powell J. Differential Geom. 131 (2025), no. 1, 199--275. |
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18. Locally flat simple spheres in CP^2
With A. Conway Bull. Lond. Math. Soc. 57 (2025), no. 1, 150–163. |
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17. The foundations of four-manifold theory in the topological category
With S. Friedl, M. Nagel and M. Powell NYJM Monogr. Volume 6, (2025) |
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16. Simple spines of homotopy 2-spheres are unique
With M. Powell Proc. London Math. Soc. (2024), 128: e12583. |
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15. Null, recursively starlike-equivalent decompositions shrink
With J. Meier and A. Ray Glasg. Math. J. 65 (2023), no. 2, 328--336. |
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14. Doubly slice knots and metabelian obstructions
With M. Powell J. Topol. Anal. 14 (2022), no. 4, 847–873. |
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13. A calculus for flow categories
With A. Lobb and D. Schütz Adv. Math. 409 (2022), part B, Paper No. 108665, 58 pp. |
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12. Abelian invariants of doubly slice links
With A. Conway Enseign. Math. 68 (2022), no. 3, pp. 243–290 |
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11. The relative Whitney trick and its applications
With C. W. Davis and J. Park Selecta Math. (N.S.) 28 (2022), no. 2, Paper No. 27, 34 pp. |
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10. Embedding spheres in knot traces
With P. Feller, A. N. Miller, M. Nagel, M. Powell and A. Ray Compos. Math. 157 (2021), no. 10, 2242--2279. |
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Me speaking about this paper at the NCNGT Conference 2020: |
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9. A lower bound for the doubly slice genus from signatures
With M. Powell New York J. Math. 27 (2021), 379–392. |
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8. Triple linking numbers and surface systems
With C. W. Davis, M. Nagel and M. Powell Indiana Univ. Math. J. 69 (2020), 2505-2547. |
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7. Khovanov homotopy calculations using flow category calculus
With A. Lobb and D. Schütz Exp. Math. 29 (2020), no. 4, 475--500. |
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6. Smooth and topological almost concordance
With M. Nagel, J. Park and M. Powell Int. Math. Res. Not. (2019), no. 23, 7324–7355. |
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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 |
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4. Framed cobordism and flow category moves
With A. Lobb and D. Schütz Algebr. Geom. Topol 18 (2018), no. 5, 2821-2858 |
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3. A Khovanov stable homotopy type for colored links
With A. Lobb and D. Schütz Algebr. Geom. Topol. 17 (2017), no. 2, 1261-1281 |
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2. Double L-groups and doubly-slice knots
Algebr. Geom. Topol. 17 (2017), no. 1, 273-329 |
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1. Twist spinning of knots and metabolizers of Blanchfield pairings
With S. Friedl Ann. Fac. Sci. Toulouse Math. (6) 24 (2015), no. 5, 1203--1218. |
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
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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.) |