5 citations · 7 across the 2 of their papers we have counts for
6 papers
Chord Diagrams and Gauss Codes for Graphs
Thomas Fleming, Blake Mellor
Chord diagrams on circles and their intersection graphs (also known as circle graphs) have been intensively studied, and have many applications to the study of knots and knot invar…
Intersection Graphs for String Links
Blake Mellor
We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via…
On the Existence of Finite Type Link Homotopy Invariants
Blake Mellor, Dylan Thurston
We show that for links with at most 5 components, the only finite type homotopy invariants are products of the linking numbers. In contrast, we show that for links with at least 9…
A few weight systems arising from intersection graphs
Blake Mellor
We show that the adjacency matrices of the intersection graphs of chord diagrams satisfy the 2-term relations of Bar-Natan and Garoufalides [bg], and hence give rise to weight syst…
Finite Type Link Concordance Invariants
Blake Mellor
This paper is a generalization of the author's previous work on link homotopy to link concordance. We show that the only real-valued finite type link concordance invariants are the…
Finite Type Link Homotopy Invariants II: Milnor's -invariants
Blake Mellor
We define a notion of finite type invariants for links with a fixed linking matrix. We show that Milnor's triple link homotopy invariant is a finite type invariant, of type 1, in t…