3 papers
math.AT2025
Cubes, cacti, and framed long knots
Robin Koytcheff, Yongheng Zhang
We define an action of the operad of projective spineless cacti on each stage of the Taylor tower for the space of framed 1-dimensional long knots in any Euclidean space. By mappin…
math.GT2025
Milnor invariants and thickness of spherical links
RafaÅ Komendarczyk, Robin Koytcheff, Fedor Manin
The ropelength of a knot or link is the minimal number of inches of 1-inch-thick rope that it takes to tie it. The relationship of this measurement to knot and link invariants has…
math.GT2024
Graphing, homotopy groups of spheres, and spaces of long links and knots
Robin Koytcheff
We study homotopy groups of spaces of long links in Euclidean space of codimension at least three. With multiple components, they admit split injections from homotopy groups of sph…