Adam S. Levine

Journal article Duke Mathematical Journal · October 15, 2022 Featured Publication Let CbZ denote the group of knots in homology spheres that bound homology balls, modulo smooth concordance in homology cobordisms. Answering a question of Matsumoto, the second author previously showed that the natural map from the sm ... Full text Cite

Khovanov homology and cobordisms between split links

Journal article Journal of Topology · September 1, 2022 Featured Publication In this paper, we study the (in)sensitivity of the Khovanov functor to 4-dimensional linking of surfaces. We prove that if (Formula presented.) and (Formula presented.) are split links, and (Formula presented.) is a cobordism between (Formula presented.) a ... Full text Cite

Khovanov homology and ribbon concordances

Journal article Bulletin of the London Mathematical Society · December 1, 2019 Featured Publication We show that a ribbon concordance between two links induces an injective map on Khovanov homology. ... Full text Cite

Khovanov homology and knot Floer homology for pointed links

Journal article Journal of Knot Theory and Its Ramifications · February 1, 2017 Featured Publication A well-known conjecture states that for any l-component link L in S3, the rank of the knot Floer homology of L (over any field) is less than or equal to 2l-1 times the rank of the reduced Khovanov homology of L. In this paper, we describe a framework that ... Full text Open Access Cite

Splicing knot complements and bordered floer homology

Journal article Journal Fur Die Reine Und Angewandte Mathematik · November 1, 2016 Featured Publication We show that the integer homology sphere obtained by splicing two nontrivial knot complements in integer homology sphere L-spaces has Heegaard Floer homology of rank strictly greater than one. In particular, splicing the complements of nontrivial knots in ... Full text Open Access Cite

NONSURJECTIVE SATELLITE OPERATORS and PIECEWISE-LINEAR CONCORDANCE

Journal article Forum of Mathematics Sigma · January 1, 2016 Featured Publication We exhibit a knot P in the solid torus, representing a generator of first homology, such that for any knot K in the 3-sphere, the satellite knot with pattern P and companion K is not smoothly slice in any homology 4-ball. As a consequence, we obtain a knot ... Full text Open Access Cite

Nonorientable surfaces in homology cobordisms

Journal article Geometry and Topology · February 27, 2015 Featured Publication We investigate constraints on embeddings of a nonorientable surface in a 4–manifold with the homology of M × I, where M is a rational homology 3–sphere. The constraints take the form of inequalities involving the genus and normal Euler class of the surface ... Full text Open Access Cite