3 papers
math.GT2026
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…
math.GT2025
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…
math.GT2024
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…