Publications and preprints

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14. Kink-equivalence of matrices, spanning surfaces, 4-manifolds, and quadratic forms (with H. Howards, W. F. Moore, and J. Tolbert), submitted, 19 pp. arXiv

13. How essential is a spanning surface?, submitted, 42 pp. arXiv

12. The virtual flyping theorem, submitted, 27 pp. arXiv

11. End-essential spanning surfaces for links in thickened surfaces, submitted, 15 pp. arXiv

10. Primeness of alternating virtual links, submitted, 32 pp. arXiv

9. A geometric proof of the flyping theorem, submitted, 51 pp. arXiv

8. A simple proof of the Crowell-Murasugi theorem, Alg. Geom. Topol. 24 (2024), no. 5, 2779-86. link

7. Efficient multisections of odd-dimensional tori, Alg. Geom. Topol. 23 (2023), no. 9, 3997-4056. link

6. Nonorientable spanning surfaces for knots, Chapter 23 of the Concise Encyclopedia of Knot Theory (2021), 197-203.

5. Crosscap numbers of alternating knots via unknotting splices, Internat. J. Math. 31 (2020), no. 7, 2050057, 30 pp. link

The knot data on my webpage comes out of this paper.

4. Alternating links have representativity 2. Alg. Geom. Topol. 18 (2018), no. 6, 3339-3362. link

3. Plumbing essential states in Khovanov homology, New York J. Math. 24 (2018), 588-610. link

2. Heegaard diagrams corresponding to Turaev surfaces (with C. Armond and N. Druivenga), J. Knot Theory Ramifications 24 (2015), no. 4, 1550026, 14 pp. link

1. A classification of spanning surfaces for alternating links (with C. Adams), Alg. Geom. Topol. 13 (2013), no. 5, 2967-3007. link