74 citations · 620 across the 41 of their papers we have counts for
42 papers
Trisection invariants of 4-manifolds are uncomputable
Nathan M. Dunfield, Marc Kegel, Shana Yunsheng Li +1
We prove that two invariants of smooth 4-manifolds defined in terms of trisections are uncomputable: the trisection genus and the Kirby-Thompson L-invariant. That is, there does no…
Ribbon concordances and slice obstructions: experiments and examples
Nathan M. Dunfield, Sherry Gong
There are 352.2 million prime knots in the 3-sphere with at most 19 crossings. We study which of these knots are slice, in both the smooth and topological categories. While no algo…
Roots of Alexander polynomials of random positive 3-braids
Nathan M. Dunfield, Giulio Tiozzo
Motivated by an observation of Dehornoy, we study the roots of Alexander polynomials of knots and links that are closures of positive 3-strand braids. We give experimental data on…
Local equivalence and refinements of Rasmussen's s-invariant
Nathan M. Dunfield, Robert Lipshitz, Dirk Schuetz
Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivaria…
1-loop equals torsion for fibered 3-manifolds
Nathan M. Dunfield, Stavros Garoufalidis, Seokbeom Yoon
In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to…
On the rank of knot homology theories and concordance
Nathan M. Dunfield, Sherry Gong, Thomas Hockenhull +2
For a ribbon knot, it is a folk conjecture that the rank of its knot Floer homology must be 1 modulo 8, and another folk conjecture says the same about reduced Khovanov homology. W…