Foliations transverse to fibers of Seifert manifolds.
Formal language theory and the geometry of 3-manifolds.
Formes hermitiennes sur les -modules
Fox pairings and generalized Dehn twists
We introduce a notion of a Fox pairing in a group algebra and use Fox pairings to define automorphisms of the Malcev completions of groups. These automorphisms generalize to the algebraic setting the action of the Dehn twists in the group algebras of the fundamental groups of surfaces. This work is inspired by the Kawazumi–Kuno generalization of the Dehn twists to non-simple closed curves on surfaces.
Fox's congruence classes and the quantum-SU(2) invariants of links in 3-manifolds.
Fractal representation of the attractive lamination of an automorphism of the free group
In this paper, we extend to automorphisms of free groups some results and constructions that classically hold for morphisms of the free monoid, i.e., the so-called substitutions. A geometric representation of the attractive lamination of a class of automorphisms of the free group (irreducible with irreducible powers (iwip) automorphisms) is given in the case where the dilation coefficient of the automorphism is a unit Pisot number. The shift map associated with the attractive symbolic lamination...
Framed holonomic knots.
Framed Links for Pfeiffer Identities.
Free and non-free subgroups of the fundamental group of the Hawaiian Earrings
The space which is composed by embedding countably many circles in such a way into the plane that their radii are given by a null-sequence and that they all have a common tangent point is called “The Hawaiian Earrings”. The fundamental group of this space is known to be a subgroup of the inverse limit of the finitely generated free groups, and it is known to be not free. Within the recent move of trying to get hands on the algebraic invariants of non-tame (e.g. non-triangulable) spaces this space...
Free group automorphisms, invariant orderings and topological applications.
Free groups of semigroups in semi-simple Lie groups.
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...
Function groups in Kleinian groups.
Functorial and algebraic properties of Browns functor.
Fundamental Group of n-sphere for n ≥ 2
Triviality of fundamental groups of spheres of dimension greater than 1 is proven, [17]
Fundamental groupoids of digraphs and graphs
We introduce the notion of fundamental groupoid of a digraph and prove its basic properties. In particular, we obtain a product theorem and an analogue of the Van Kampen theorem. Considering the category of (undirected) graphs as the full subcategory of digraphs, we transfer the results to the category of graphs. As a corollary we obtain the corresponding results for the fundamental groups of digraphs and graphs. We give an application to graph coloring.
Fundamental Groups, ...-groups and Codimension two Submanifolds
Fundamental pro-groupoids and covering projections
We introduce a new notion of covering projection E → X of a topological space X which reduces to the usual notion if X is locally connected. We use locally constant presheaves and covering reduced sieves to find a pro-groupoid π crs (X) and an induced category pro (π crs (X), Sets) such that for any topological space X the category of covering projections and transformations of X is equivalent to the category pro (π crs (X), Sets). We also prove that the latter category is equivalent to pro (π CX,...