6 papers · 1 filter
Ribbon concordance and cabling
Jennifer Hom, JungHwan Park
We study ribbon concordances to cable knots. We formulate a conjecture predicting that any nontrivial knot admitting a ribbon concordance to a (p,q)-cable must itself be a (p,q)-ca…
Smooth Realizations of Line Configurations
Paolo Aceto, Duncan McCoy, JungHwan Park
We study the problem of realizing line configurations as collections of 2-spheres smoothly embedded in the complex projective plane. Building upon prior work by Ruberman and Starks…
Isotopy and equivalence of knots in 3-manifolds
Paolo Aceto, Corey Bregman, Christopher W. Davis +2
We show that in a prime, closed, oriented 3-manifold M, equivalent knots are isotopic if and only if the orientation preserving mapping class group is trivial. In the case of irred…
Handle decomposition complexity and representation spaces
Paolo Aceto, Aliakbar Daemi, Jennifer Hom +2
We prove that there are homology three-spheres that bound definite four-manifolds, but any such bounding four-manifold must be built out of many handles. The argument uses the homo…
Definite fillings of lens spaces
Paolo Aceto, Duncan McCoy, JungHwan Park
This paper considers the problem of determining the smallest (as measured by the second Betti number) smooth negative-definite filling of a lens space. The main result is to classi…
The -cable of the figure-eight knot is not smoothly slice
Irving Dai, Sungkyung Kang, Abhishek Mallick +2
We prove that the -cable of the figure-eight knot is not smoothly slice by showing that its branched double cover bounds no equivariant homology ball.