7 papers · 1 filter
Unknotting orientable surfaces
Anthony Conway
It is shown that every locally flatly embedded genus surface in the -sphere with knot group is unknotted. The same proof establishes that any two ge…
Non-smoothable surfaces in the 4-sphere
Anthony Conway, Daniel Galvin
We construct examples of non-smoothable surfaces in the -sphere, thereby answering Question 4.32 on the K3 problem list. These surfaces are non-orientable and have knot group of…
Simply slicing knots
Anthony Conway, Patrick Orson, Mark Pencovitch
Given a simply-connected 4-manifold with boundary the 3-sphere, this paper establishes sufficient conditions for a knot in the boundary to be sliced by a locally flat disc in the 4…
Immersed surfaces with knot group
Anthony Conway, Allison N. Miller
This article is concerned with locally flatly immersed surfaces in simply-connected -manifolds where the complement of the surface has fundamental group . Once the g…
-disks in
Anthony Conway, Irving Dai, Maggie Miller
We study locally flat disks in with boundary a fixed knot and whose complement has fundamental group $\mathbb…
Locally flat simple spheres in
Anthony Conway, Patrick Orson
The fundamental group of the complement of a locally flat surface in a -manifold is called the knot group of the surface. In this article we prove that two locally flat -sphe…
A criterion for double sliceness
Anthony Conway
We describe a condition involving noncommutative Alexander modules which ensures that a knot with Alexander module $\mathbb{Z}[t^{\pm 1}]/(t-2) \oplus \mathbb{Z}[t^{\pm 1}]/(t^{-1}…