Finite type invariants of integral homology 3-spheres: A survey
Fixed points and braids.
Flat hierarchy
We consider the hierarchy flats, a combinatorial generalization of flat virtual links proposed by Louis Kauffman. An approach to constructing invariants for hierarchy flats is presented; several examples are given.
Flows on supporting all links as orbits.
Fox's congruence classes and the quantum-SU(2) invariants of links in 3-manifolds.
Framed holonomic knots.
Framed Links for Pfeiffer Identities.
Free group automorphisms, invariant orderings and topological applications.
Frobenius algebras and skein modules of surfaces in 3-manifolds
For each (commutative) Frobenius algebra there is defined a skein module of surfaces embedded in a given 3-manifold and bounding a prescribed curve system in the boundary. The skein relations are local and generate the kernel of a certain natural extension of the corresponding topological quantum field theory. In particular the skein module of the 3-ball is isomorphic to the ground ring of the Frobenius algebra. We prove a presentation theorem for the skein module with generators incompressible...
Generalized Chern-Simons theory and skein relations in arbitrary dimensions
Generalized Montesinos knots, tunnels and N-torsion.
Generalized n-colorings of links
The notion of an (n,r)-coloring for a link diagram generalizes the idea of an n-coloring introduced by R. H. Fox. For any positive integer n the various (n,r)-colorings of a diagram for an oriented link l correspond in a natural way to the periodic points of the representation shift of the link. The number of (n,r)-colorings of a diagram for a satellite knot is determined by the colorings of its pattern and companion knots together with the winding number.
Generic immersions of curves, knots, monodry and Gordian number
Genus 2 Heegaard decompositions of small Seifert manifolds
The genus 2 Heegaard splittings and decompositions of Seifert manifolds over with 3 exeptional fibres are classified with respect to isotopies and homeomorphisms. In general there are 3 different isotopy classes of Heegaard splittings and 6 different isotopy classes of Heegaard decompositions. Moreover, we determine when a homeomorphism class is not an isotopy class.
Geodesic knots in the figure-eight knot complement.
Geodesic surfaces in knot complements.
Geometric invariants of link cobordism.
Geometric presentations of classical knot groups.
Geometric types of twisted knots
Let be a knot in the -sphere , and a disk in meeting transversely in the interior. For non-triviality we assume that over all isotopies of in . Let () be a knot obtained from by twistings along the disk . If the original knot is unknotted in , we call a twisted knot. We describe for which pair and an integer , the twisted knot is a torus knot, a satellite knot or a hyperbolic knot.
Geometrically fibred two-knots.