Free group automorphisms, invariant orderings and topological applications.
Free groups of semigroups in semi-simple Lie groups.
Free Involutions.
Free subgroups of diffeomorphism groups
Frobenius algebras and ambidextrous adjunctions.
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.
Function spaces and adjoints.
Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups
Functor of extension in Hilbert cube and Hilbert space
It is shown that if Ω = Q or Ω = ℓ 2, then there exists a functor of extension of maps between Z-sets in Ω to mappings of Ω into itself. This functor transforms homeomorphisms into homeomorphisms, thus giving a functorial setting to a well-known theorem of Anderson [Anderson R.D., On topological infinite deficiency, Michigan Math. J., 1967, 14, 365–383]. It also preserves convergence of sequences of mappings, both pointwise and uniform on compact sets, and supremum distances as well as uniform continuity,...
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 group of with no circle action
We show that can be nontrivial for that does not admit any symplectic circle action.
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,...
Fundamental vector fields on associated fiber bundles
Fundamental vector fields on type fibres of jet prolongations of tensor bundles
-homologie et -homologie dans la catégorie des -modules différentiables
-variétés topologiques et -microfibrés