32 citations · 169 across the 18 of their papers we have counts for
19 papers
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 (…
Equivariant hyperbolization of -manifolds via homology cobordisms
Dave Auckly, Hee Jung Kim, Paul Melvin +1
The main result of this paper is that any -dimensional manifold with a finite group action is equivariantly, invertibly homology cobordant to a hyperbolic manifold; this result…
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…
Equivariant Corks
Dave Auckly, Hee Jung Kim, Paul Melvin +1
For suitable finite groups G, we construct contractible 4-manifolds C with an effective G-action on whose associated pairs (C,g) for all are distinct smoothi…
Stable isotopy in four dimensions
Dave Auckly, Hee Jung Kim, Paul Melvin +1
We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing…
Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows, Part 2
Dennis DeTurck, Herman Gluck, Rafal Komendarczyk +4
We describe a new approach to triple linking invariants and integrals, aiming for a simpler, wider and more natural applicability to the search for higher order helicities of fluid…