Group Actions Having One Fixed Point.
John Ewing, Robert Stong (1986)
Mathematische Zeitschrift
Allan L. Edmonds, Charles Livingston (1983)
Commentarii mathematici Helvetici
J.F. Davis, S. Weinberger (1986)
Inventiones mathematicae
Reinhard Schultz (1981)
Journal für die reine und angewandte Mathematik
Karl Heinz Mayer (1991)
Mathematische Annalen
Stefano De Michelis (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
We study the homology of the fixed point set on a rational homology sphere under the action of a finite group.
Dariusz M. Wilcznski (1988)
Mathematische Annalen
Krzysztof Fawalowski (1984)
Mathematische Zeitschrift
William J. Floyd (1980)
Inventiones mathematicae
Pierre Will (2006/2007)
Séminaire de théorie spectrale et géométrie
Nous présentons quelques résultats au sujet des groupes engendrés par trois involutions antiholomorphes dans le cadre du plan hyperbolique complexe .
T. Jakubowski (1980)
Colloquium Mathematicae
Richard Millman (1975)
Fundamenta Mathematicae
Matthew G. Brin, Craig C. Squier (1985)
Inventiones mathematicae
Yoshifumi Matsuda (2009)
Annales de l’institut Fourier
We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the -topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.
A.M. Amores (1982)
Collectanea Mathematica
S.R. Kulkarni (1978)
Mathematische Annalen
Hanspeter Fischer, David G. Wright (2003)
Fundamenta Mathematicae
Hass, Rubinstein, and Scott showed that every closed aspherical (irreducible) 3-manifold whose fundamental group contains the fundamental group of a closed aspherical surface, is covered by Euclidean space. This theorem does not generalize to higher dimensions. However, we provide geometric tools with which variations of this theorem can be proved in all dimensions.
Rainer Löwen (1978)
Mathematische Annalen
A. Degtyarev, V. Kharlamov (1996)
Commentarii mathematici Helvetici
László Verhóczki (2012)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
The exceptional compact symmetric spaces and admit cohomogeneity one isometric actions with two totally geodesic singular orbits. These singular orbits are not reflective submanifolds of the ambient spaces. We prove that the radial unit vector fields associated to these isometric actions are harmonic and minimal.