5 citations · 6 across the 4 of their papers we have counts for
8 papers · 1 filter
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 stu…
Corks, covers, and complex curves
Kyle Hayden
We show that contains pairs of properly embedded, smooth complex curves that are isotopic through homeomorphisms but not diffeomorphisms of . The const…
New curiosities in the menagerie of corks
Kyle Hayden, Lisa Piccirillo
A cork is a smooth, contractible, oriented, compact 4-manifold together with a self-diffeomorphism of the boundary 3-manifold that cannot extend to a self-diffeomorphism of…
Exotically knotted disks and complex curves
Kyle Hayden
This paper studies properly embedded surfaces in the 4-ball that are exotically knotted (i.e., topologically but not smoothly isotopic), and leverages this local phenomenon to stud…
The trace embedding lemma and spinelessness
Kyle Hayden, Lisa Piccirillo
We demonstrate new applications of the trace embedding lemma to the study of piecewise-linear surfaces and the detection of exotic phenomena in dimension four. We provide infinitel…
Exotic Mazur manifolds and knot trace invariants
Kyle Hayden, Thomas E. Mark, Lisa Piccirillo
From a handlebody-theoretic perspective, the simplest compact, contractible 4-manifolds, other than the 4-ball, are Mazur manifolds. We produce the first pairs of Mazur manifolds t…