Endliche Erweiterungen nichteuklidischer kristallographischer Gruppen.
Eine Verallgemeinerung der Formel von Riemann-Hurwitz.
Surfaces and the Second Homology of a Group.
Das Nielsensche Realisierungsproblem für hinreichend große 3-Mannigfaltigkeiten.
Periodische Homöomorhismen Seifertscher Faserräume.
Nielsensche Realisierungssätze für Seifertfaserungen.
Über Gruppen von Homöomorphismen Seifertscher Faserräume und flacher Manigfaltigkeiten.
Über Homöomorphismen n-dimensionaler Henkelkörper und endliche Erweiterungen von Schottky-Gruppen.
Free products with amalgamation of finite groups and finite outer automorphism groups of free groups
Endliche Gruppen von Abbildungsklassen gefaserter 3-Mannigfaltigkeiten.
Symmetries of Nonelliptic Montesinos Links.
Über Erweiterungen von Z und Z2 * Z2 durch nichteuklidische kristallographische Gruppen.
The ?-orbifold Group of a Link.
The maximum order of finite groups of outer automorphisms of free groups.
On finite groups acting on acyclic low-dimensional manifolds
We consider finite groups which admit a faithful, smooth action on an acyclic manifold of dimension three, four or five (e.g. Euclidean space). Our first main result states that a finite group acting on an acyclic 3- or 4-manifold is isomorphic to a subgroup of the orthogonal group O(3) or O(4), respectively. The analogous statement remains open in dimension five (where it is not true for arbitrary continuous actions, however). We prove that the only finite nonabelian simple groups admitting a smooth...
Cyclic branched coverings and homology 3-spheres with large group actions
We show that, if the covering involution of a 3-manifold M occurring as the 2-fold branched covering of a knot in the 3-sphere is contained in a finite nonabelian simple group G of diffeomorphisms of M, then M is a homology 3-sphere and G isomorphic to the alternating or dodecahedral group 𝔸₅ ≅ PSL(2,5). An example of such a 3-manifold is the spherical Poincaré sphere. We construct hyperbolic analogues of the Poincaré sphere. We also give examples of hyperbolic ℤ₂-homology 3-spheres with PSL(2,q)-actions,...
On finite groups acting on a connected sum of 3-manifolds S² × S¹
Let denote the closed 3-manifold obtained as the connected sum of g copies of S² × S¹, with free fundamental group of rank g. We prove that, for a finite group G acting on which induces a faithful action on the fundamental group, there is an upper bound for the order of G which is quadratic in g, but there does not exist a linear bound in g. This implies then a Jordan-type bound for arbitrary finite group actions on which is quadratic in g. For the proofs we develop a calculus for finite group...
On finite groups of isometries of handlebodies in arbitrary dimensions and finite extensions of Schottky groups
It is known that the order of a finite group of diffeomorphisms of a 3-dimensional handlebody of genus g > 1 is bounded by the linear polynomial 12(g-1), and that the order of a finite group of diffeomorphisms of a 4-dimensional handlebody (or equivalently, of its boundary 3-manifold), faithful on the fundamental group, is bounded by a quadratic polynomial in g (but not by a linear one). In the present paper we prove a generalization for handlebodies of arbitrary dimension d, uniformizing handlebodies...
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