Families of algebraic curves with nodes
Families of polynomials with total Milnor number constant.
Fatgraph models of RNA structure
In this review paper we discuss fatgraphs as a conceptual framework for RNA structures. We discuss various notions of coarse-grained RNA structures and relate them to fatgraphs.We motivate and discuss the main intuition behind the fatgraph model and showcase its applicability to canonical as well as noncanonical base pairs. Recent discoveries regarding novel recursions of pseudoknotted (pk) configurations as well as their translation into context-free grammars for pk-structures are discussed. This...
Fibred closed braids with disc-band fibre surfaces
A classical result by Stallings provides a necessary and sufficient condition to decide whether a given embedded surface is a fibre in . In this paper it is described how to find a candidate fibre surface for a a link presented as a closed braid. Also it is described an implemented algorithm to find the main ingredients of the necessary and sufficient condition of Stallings, namely presentations of the fundamental groups of the surface and of its complement in , and an explicit expression of...
Fibred Knots and Disks with Clasps.
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...