5 papers
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…
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…
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…
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…
A unified Casson-Lin invariant for the real forms of SL(2)
Nathan M. Dunfield, Jacob Rasmussen
We introduce a unified framework for counting representations of knot groups into and . For a knot in the 3-sphere, Lin and others showed that a Cass…