8 citations · 22 across the 7 of their papers we have counts for
9 papers · 1 filter
Doubles of Gluck twists: a five dimensional approach
David Gabai, Patrick Naylor, Hannah Schwartz
Using a 5-dimensional perspective, we balance algebraic and geometric handle cancellation to show that doubles of Gluck twists of certain 2-spheres with two minima are standard. Th…
A 4-dimensional light bulb theorem for disks
Hannah Schwartz
We give a 4-dimensional light bulb theorem for properly embedded disks, generalizing recent work of Gabai and Kosanovic-Teichner in certain contexts, and extending the 4-dimensiona…
Duals of non-zero square
Hannah R. Schwartz
In this short note, for each non-zero integer n, we construct a 4-manifold containing a smoothly concordant pair of spheres with a common dual of square n but no automorphism carry…
Gluck twisting roll spun knots
Patrick Naylor, Hannah Schwartz
We show that the smooth homotopy 4-sphere obtained by Gluck twisting the m-twist n-roll spin of any unknotting number one knot is diffeomorphic to the standard 4-sphere, for any pa…
Unknotting numbers of 2-spheres in the 4-sphere
Jason Joseph, Michael Klug, Benjamin Ruppik +1
We compare two naturally arising notions of unknotting number for 2-spheres in the 4-sphere: namely, the minimal number of 1-handle stabilizations needed to obtain an unknotted sur…
Higher order corks
Paul Melvin, Hannah Schwartz
It is shown that any finite list of smooth closed simply-connected 4-manifolds homeomorphic to a given one X can be obtained by removing a single compact contractible submanifold (…
A note on the complexity of h-cobordisms
Hannah R. Schwartz
We show that the number of double points of smoothly immersed 2-spheres representing certain homology classes of an oriented, smooth, closed, simply-connected 4-manifold X must inc…
Equivalent non-isotopic spheres in 4-manifolds
Hannah R. Schwartz
We construct infinitely many smooth oriented 4-manifolds containing pairs of homotopic, smoothly embedded 2-spheres that are not topologically isotopic, but that are equivalent by…
Isotopy of surfaces in 4-manifolds after a single stabilization
Dave Auckly, Hee Jung Kim, Paul Melvin +2
Any two homologous surfaces of the same genus embedded in a smooth 4-manifold X with simply-connected complements are shown to be smoothly isotopic in the connected sum of X and th…