5 citations · 5 across the 1 of their papers we have counts for
6 papers
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…
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…
The Conway knot is not slice
Lisa Piccirillo
A knot is said to be slice if it bounds a smooth properly embedded disk in the 4-ball. We demonstrate that the Conway knot, 11n34 in the Rolfsen tables, is not slice. This complete…
Shake genus and slice genus
Lisa Piccirillo
An important difference between high dimensional smooth manifolds and smooth 4-manifolds that in a 4-manifold it is not always possible to represent every middle dimensional homolo…
On the Stein framing number of a knot
Thomas E. Mark, Lisa Piccirillo, Faramarz Vafaee
For an integer , write for the 4-manifold obtained by attaching a 2-handle to the 4-ball along the knot with framing . It is known that if $n< \overli…