16 citations · 19 across the 4 of their papers we have counts for
6 papers
Relative Thom Conjectures, symplectic and beyond
Matthew Hedden, Katherine Raoux
We establish a criterion that ensures a bounded almost complex curve in a bounded almost complex 4-manifold minimizes genus amongst all smooth surfaces that share its homology clas…
A 4-dimensional rational genus bound
Katherine Raoux, Matthew Hedden
We introduce a 4-dimensional analogue of the rational Seifert genus of a knot , which we call the rational slice genus, that measures the complexity of a homology class…
4-dimensional aspects of tight contact 3-manifolds
Matthew Hedden, Katherine Raoux
In this article we conjecture a 4-dimensional characterization of tightness: a contact structure is tight if and only if a slice-Bennequin inequality holds for smoothly embedded su…
Knot Floer homology and relative adjunction inequalities
Matthew Hedden, Katherine Raoux
We establish inequalities that constrain the genera of smooth cobordisms between knots in 4-dimensional cobordisms. These "relative adjunction inequalities" improve the adjunction…
Braids, fibered knots, and concordance questions
Diana Hubbard, Keiko Kawamuro, Feride Ceren Kose +5
Given a knot in , one can associate to it a surface diffeomorphism in two different ways. First, an arbitrary knot in can be represented by braids, which can be though…
-invariants for knots in rational homology spheres
Katherine Raoux
Ozsváth and Szabó used the knot filtration on to define the -invariant for knots in the 3-sphere. In this article, we generalize their construction and defin…