5 papers
-complexes, Clasp Number, and Triple Linking Number
Christopher William Davis, David Lawrence, Jack Paulsen +1
A C-complex is a union of Seifert surfaces for the components of a link which intersect each other in clasps. The clasp number of a link is the minimal number of clasps amongst all…
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…
Lifting Milnor Invariants for 3-Component Links
Christopher W. Davis, JungHwan Park
We define a sequence of integer-valued invariants $γ^k(L)$ for a -component link . We prove that the resulting -invariants are invariant under concordance, and more gene…
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…
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, \(n_Î(L)\), are invariants of the link homotopy class of \(L\) which count how many cross…