arXiv subjects
Publications and source records attributed to Abdelouahab Arouche.
We study the representations of the commutator subgroup K_{n} of the braid group B_{n} into a finite group . This is done through a symbolic dynamical system. Some experimental results enable us to compute the number of subgroups of K_{n} of a given (finite) index, and, as a by-product, to recover the well known fact that every representation of K_{n} into S_{r}, with n > r, must be trivial.
We study the representations of the commutator subgroup of the braid group with n strands in the symmetric group of degree r. Motivated by some experimental results, we conjecture that for n>r, every such representation is trivial.
We give an explicit decription for univeral principal U(r)-bundles with periodic map by means of equivariant Stiefel manifolds. We then show that the associated equivariant vector bundle is equivalent to the canonical one given by G. Segal. Finally, we investigate some ideals involved in the equivariant K-theory of this classifying space.
An important ingredient in the completion theorem of equivariant K-theory given by S. Jackowski is that the representation ring R(Gamma) of a compact Lie group satisfies two restriction properties called (N) and (R\_{F}). We give in this note sufficient conditions on a (compact) -space Z such that these properties hold with K\_{Gamma}^{*}(Z) instead of R(Gamma). As an example, we consider the space Z(Gamma;G) of the so called "elementary cocycles with coefficients in G" invented by H. Ibisch in his construction of a universal (Gamma;G)-bundle.
We show a geometric rigidity of isometric actions of non compact (semisimple) Lie groups on Lorentz manifolds. Namely, we show that the manifold has a warped product structure of a Lorentz manifold with constant curvature by a Riemannian manifold.