12 citations · 40 across the 17 of their papers we have counts for
21 papers
Dehn surgery functions are never injective
Kyle Hayden, Lisa Piccirillo, Laura Wakelin
We prove that, for each fixed rational number , there exists a pair of distinct knots whose -surgeries are orientation-preservingly homeomorphic. This conf…
Lecture notes on link homologies and knotted surfaces
Kyle Hayden
Link homology theories (such as knot Floer homology and Khovanov homology) have become indispensable tools for studying knots and links, including powerful 4-dimensional obstructio…
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…
Exotic aspherical 4-manifolds
Michael Davis, Kyle Hayden, Jingyin Huang +2
We construct closed, aspherical, smooth 4-manifolds that are homeomorphic but not diffeomorphic. These provide counterexamples to a smooth analog of the Borel conjecture in dimensi…
Doubled Disks and Satellite Surfaces
Gary Guth, Kyle Hayden, Sungkyung Kang +1
Conjecturally, a knot is slice if and only if its positive Whitehead double is slice. We consider an analogue of this conjecture for slice disks in the four-ball: two slice disks o…
One stabilization is not enough for closed knotted surfaces
Kyle Hayden, Sungkyung Kang, Anubhav Mukherjee
In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either exter…