5 papers
Planar multilinks and rational singularities
Márton Beke, Olga Plamenevskaya
Fibered multilinks are a generalization of classical fibered knots and open books that arise in the study of surface singularities and Milnor fibrations. We prove that if the canon…
Minimal rational graphs admitting a QHD smoothing
Márton Beke, Márton Beke
Using the picture deformation technique of De Jong-Van Straten we show that no singularity whose resolution graph has 3 or 4 large nodes, i.e., nodes satisfying d(v)+e(v)\leq -2, h…
An Unexpected Rational Blowdown
Márton Beke, Olga Plamenevskaya, Laura Starkston
The rational blowdown operation in 4-manifold topology replaces a neighborhood of a configuration of spheres by a rational homology ball. Such configurations typically arise from r…
A knot-theoretic tour of dimension four
Márton Beke, Kyle Hayden
These notes follow a lecture series at the "Singularities and low dimensional topology" winter school at the Rényi Institute in January 2023, with a target audience of graduate st…
New Exotic four-manifolds with fundamental group
Márton Beke, László Koltai, Sarah Zampa
We extend a construction of Stipsicz-Szabó of infinitely many irreducible exotic smooth structures of some closed four-manifolds with even and fundamental group $\mathbb{Z…