Global knot theory in F2 x R
Thomas Fiedler
Abstract
We introduce a special class of knots, called global knots, in F2 x R and we construct new isotopy invariants, called T-invariants, for global knots. Some T-invariants are of finite type but they cannot be extracted from the generalized Kontsevitch integral (which is consequently not the universal invariant of finite type for the restricted class of global knots). We prove that T-invariants separate all global knots of a certain type. As a corollary, we prove the non-invertibility of some links in S3 without making any use of the link group.
Create a lesson
Related papers
Chromatic Spherical and Renormalized Reshetikhin-Turaev Invariants for Drinfeld Centers
Nicolas Bridges, Shawn Cui, Nathan Geer
3-manifold decision problems and Riemann hypotheses
John A. Baldwin, Steven Sivek
On the (in)finiteness of fixed characters in genus 3
Yixuan Fu
Non-Pseudo-Arithmetic Hyperbolic 4-Manifolds
Alexander Kolpakov
Convex ribbon disks, quasipositivity, and Lagrangian sliceness
Joseph Breen, Alexander Zupan
A Smooth Shioda-Tate Isomorphism for Elliptically Fibered 4-Manifolds
Maria Morariu