New adventures in the land of -analogues (Yang-Baxter equations). (Nouvelles aventures au pays des -analogues (équation de Yang-Baxter).)
Noncommutative independence in the infinite braid and symmetric group
This is an introductory paper about our recent merge of a noncommutative de Finetti type result with representations of the infinite braid and symmetric group which allows us to derive factorization properties from symmetries. We explain some of the main ideas of this approach and work out a constructive procedure to use in applications. Finally we illustrate the method by applying it to the theory of group characters.
Non-positively curved aspects of Artin groups of finite type.
Non-standard automorphisms of branched coverings of a disk and a sphere
Let Y be a closed 2-dimensional disk or a 2-sphere. We consider a simple, d-sheeted branched covering π: X → Y. We fix a base point A₀ in Y (A₀ ∈ ∂Y if Y is a disk). We consider the homeomorphisms h of Y which fix ∂Y pointwise and lift to homeomorphisms ϕ of X-the automorphisms of π. We prove that if Y is a sphere then every such ϕ is isotopic by a fiber-preserving isotopy to an automorphism which fixes the fiber pointwise. If Y is a disk, we describe explicitly a small set of automorphisms of...
Normal all pseudo-Anosov subgroups of mapping class groups.
Numerical invariants of exponential groups and locally free approximation of the braid group.