4 papers
Constructing knots with low rational genera
Clayton McDonald, Allison N. Miller
We give a flexible construction for knots in the 3-sphere that bound surfaces of unexpectedly low genus in punctured open books on 3-manifolds. We use this construction to give the…
Not all knots are smoothly round handle slice
Tye Lidman, Allison N. Miller, Arunima Ray
Freedman and Krushkal showed that if the surgery conjecture and the -cobordism conjecture hold for all topological 4-manifolds, then every link with pairwise zero linking number…
Slice disks modulo local knotting
Jeffrey Meier, Allison N. Miller
The second author and Powell asked whether there exist knots bounding infinitely many slice disks that remain pairwise nonisotopic, even after local knotting. We answer this questi…
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…