We prove that for each integer there is an open neighborhood of the identity map of the 2-sphere , in topology such that: if is a nilpotent subgroup of with length of nilpotency, generated by elements in , then the natural -action on has nonempty fixed point set. Moreover, the -action has at least two fixed points if the action has a finite nontrivial orbit.
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.
We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions on a concrete realization of the universal covering group of . We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to , and corresponding to the eigenvalue .
We show that a surface group of high genus contained in a classical simple Lie group can be deformed to become Zariski dense, unless the Lie group is (resp. , odd) and the surface group is maximal in some (resp. ). This is a converse, for classical groups, to a rigidity result of S. Bradlow, O. García-Prada and P. Gothen.
Cet article est consacré à l’étude d’une large classe de flots d’Anosov sur les variétés graphées. Nous établissons un résultat général à propos des plongements de variétés de Seifert dans les variétés de dimension 3 admettant un flot d’Anosov produit, généralisant ainsi un résultat de E. Ghys. Nous montrons que, à isotopie près, la restriction du feuilletage unidimensionnel défini par le flot à l’image de ce plongement est topologiquement conjugué à un morceau de flot géodésique privé d’un nombre...