11 citations · 62 across the 26 of their papers we have counts for
6 papers · 1 filter
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…
Torsion in the knot concordance group and cabling
Sungkyung Kang, JungHwan Park
We define a nontrivial mod 2 valued additive concordance invariant defined on the torsion subgroup of the knot concordance group using involutive knot Floer package. For knots not…
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.
Unknotting number and cabling
Jennifer Hom, Tye Lidman, JungHwan Park
The unknotting number of knots is a difficult quantity to compute, and even its behavior under basic satelliting operations is not understood. We establish a lower bound on the unk…
Seifert surfaces in the 4-ball
Kyle Hayden, Seungwon Kim, Maggie Miller +2
We answer a question of Livingston from 1982 by producing Seifert surfaces of the same genus for a knot in that do not become isotopic when their interiors are pushed into $B…