Das Nielsensche Realisierungsproblem für hinreichend große 3-Mannigfaltigkeiten.
Let with and let be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of ? (Classically, for and more recently also for general .) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially prove...
Let be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup of ℳ(N) generated...
Nous présentons un algorithme permettant de convertir une présentation de variété de dimension 3 comme revêtement simple à trois feuillets de la sphère en une présentation de chirurgie.