25 citations · 53 across the 12 of their papers we have counts for
15 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…
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 constructions and invariants of closed exotic 4-manifolds
Adam Simon Levine, Tye Lidman, Lisa Piccirillo
In this article, we give new means of constructing and distinguishing closed exotic four-manifolds. Using Heegaard Floer homology, we define new closed four-manifold invariants tha…
Small symplectic caps and embeddings of homology balls in the complex projective plane
John B. Etnyre, Hyunki Min, Lisa Piccirillo +1
We present a handlebody construction of small symplectic caps, and hence of small closed symplectic 4-manifolds. We use this to construct handlebody descriptions of symplectic embe…
-manifolds with boundary and fundamental group
Anthony Conway, Lisa Piccirillo, Mark Powell
We classify topological -manifolds with boundary and fundamental group , under some assumptions on the boundary. We apply this to classify surfaces in simply-connect…
From zero surgeries to candidates for exotic definite four-manifolds
Ciprian Manolescu, Lisa Piccirillo
One strategy for distinguishing smooth structures on closed -manifolds is to produce a knot in that is slice in one smooth filling of but not slice in some h…
Relative genus bounds in indefinite four-manifolds
Ciprian Manolescu, Marco Marengon, Lisa Piccirillo
Given a closed four-manifold with an indefinite intersection form, we consider smoothly embedded surfaces in int, with boundary a knot . We…
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…
Knot traces and concordance
Allison N. Miller, Lisa Piccirillo
We give a method for constructing many pairs of distinct knots and such that the two 4-manifolds obtained by attaching a 2-handle to along with framing zero…