31 citations · 56 across the 14 of their papers we have counts for
18 papers
Bar cohomology of links: beyond Milnor invariants
Greg Friedman, Nir Gadish, Robin Koytcheff +2
We develop bar cohomology of link complements as an invariant of links in homology spheres. In this setting, bar cohomology is a Hopf algebra which is calculable using surfaces and…
Milnor invariants and thickness of spherical links
Rafał 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…
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…
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…
Diagrams for primitive cycles in spaces of pure braids and string links
Rafal Komendarczyk, Robin Koytcheff, Ismar Volic
The based loop space of a configuration space of points in a Euclidean space can be viewed as a space of pure braids in a Euclidean space of one dimension higher. We continue our s…
Spaces of knots in the solid torus, knots in the thickened torus, and links in the 3-sphere
Andrew Havens, Robin Koytcheff
We recursively determine the homotopy type of the space of any irreducible framed link in the 3-sphere, modulo rotations. This leads us to the homotopy type of the space of any kno…