32 citations · 124 across the 25 of their papers we have counts for
29 papers
Smoothly knotted surfaces that remain distinct after many internal stabilizations
David Auckly
Internal stabilization adds a trivial handle to an embedded surface in a coordinate chart. It is known that any pair of smoothly knotted surfaces in a simply-connected -manifold…
Branched covering simply-connected 4-manifolds
David Auckly, R. Inanc Baykur, Roger Casals +3
We prove that any closed simply-connected smooth 4-manifold is 16-fold branched covered by a product of an orientable surface with the 2-torus, where the construction is natural wi…
Folklore, the Borromean rings, the icosahedron, and three dimensions
Dave Auckly
There is a relationship between the Borromean rings, the icosahedron and something called the Poincaré homology sphere. This relationship is explored in a wandering path that intro…
On non-orientable surfaces in 4-manifolds
David Auckly, Rustam Sadykov
We find conditions under which a non-orientable closed surface S embedded into an orientable closed 4-manifold X can be represented by a connected sum of an embedded closed surface…
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…