5 citations · 5 across the 3 of their papers we have counts for
9 papers · 1 filter
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…
Distinguishing closed 4-manifolds by slicing
Tye Lidman, Lisa Piccirillo
One approach to produce a pair of homeomorphic-but-not-diffeomophic closed 4-manifolds is to find a knot which is smoothly slice in one but not the other. This approach has never b…
Stably irreducible non-orientable knotted surfaces
Tye Lidman, Lisa Piccirillo
We give an elementary obstruction to reducibility for knotted surfaces in the four-sphere. As a new application, we construct stably irreducible non-orientable surfaces.
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…