2 citations · 2 across the 5 of their papers we have counts for
7 papers · 1 filter
Gordian distance and clasper surgery for links
Anthony Bosman, Christopher W. Davis, Taylor Martin +1
In 2000, Habiro introduced the notion of -equivalence of knots and links. This geometric filtration is closely connected to finite type invariants, a class of invariants inclu…
Rectangular mosaics for virtual knots
Taylor Martin, Rachel Meyers
Mosaic knots, first introduced in 2008 by Lomanoco and Kauffman, have become a useful tool for studying combinatorial invariants of knots and links. In 2020, by considering knot mo…
How many crossing changes or Delta-moves does it take to get to a homotopy trivial link?
Anthony Bosman, Christopher William Davis, Taylor Martin +2
The homotopy trivializing number, \(n_h(L)\), and the Delta homotopy trivializing number, \(n_Δ(L)\), are invariants of the link homotopy class of \(L\) which count how many crossi…
Moves relating C-complexes: A correction to Cimasoni's "A geometric construction of the Conway potential function"
Christopher William Davis, Taylor Martin, Carolyn Otto
In groundbreaking work from 2004, Cimasoni gave a geometric computation of the multivariable Conway potential function in terms of a generalization of a Seifert surface for a link…
Splittings of link concordance groups
Taylor E. Martin, Carolyn Otto
We establish several results about two short exact sequences involving lower terms of the -solvable filtration, of the string link concordance group $\math…
Every genus one algebraically slice knot is 1-solvable
Christopher W. Davis, Taylor E. Martin, Carolyn Otto +1
Cochran, Orr, and Teichner developed a filtration of the knot concordance group indexed by half integers called the solvable filtration. Its terms are denoted by . I…
Classification of Links Up to 0-Solvability
Taylor E. Martin
The -solvable filtration of the -component smooth (string) link concordance group, $$\dots \subset \mathcal{F}^m_{n+1} \subset \mathcal{F}^m_{n.5} \subset \mathcal{F}^m_n \do…