ترغب بنشر مسار تعليمي؟ اضغط هنا

Transitive actions of locally compact groups on locally contractible spaces

176   0   0.0 ( 0 )
 نشر من قبل Linus Kramer
 تاريخ النشر 2013
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group.



قيم البحث

اقرأ أيضاً

We study abstract group actions of locally compact Hausdorff groups on CAT(0) spaces. Under mild assumptions on the action we show that it is continuous or has a global fixed point. This mirrors results by Dudley and Morris-Nickolas for actions on tr ees. As a consequence we obtain a geometric proof for the fact that any abstract group homomorphism from a locally compact Hausdorff group into a torsion free CAT(0) group is continuous.
230 - Linus Kramer 2014
We prove continuity results for abstract epimorphisms of locally compact groups onto finitely generated groups.
We are concerned with questions of the following type. Suppose that $G$ and $K$ are topological groups belonging to a certain class $cal K$ of spaces, and suppose that $phi:K to G$ is an abstract (i.e. not necessarily continuous) surjective group hom omorphism. Under what conditions on the group $G$ and the kernel is the homomorphism $phi$ automatically continuous and open? Questions of this type have a long history and were studied in particular for the case that $G$ and $K$ are Lie groups, compact groups, or Polish groups. We develop an axiomatic approach, which allows us to resolve the question uniformly for different classes of topological groups. In this way we are able to extend the classical results about automatic continuity to a much more general setting.
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with open normali ser, and show that its properties reflect the global structure of the ambient group.
177 - Pekka Salmi 2011
We define the notion of rough Cayley graph for compactly generated locally compact groups in terms of quasi-actions. We construct such a graph for any compactly generated locally compact group using quasi-lattices and show uniqueness up to quasi-isom etry. A class of examples is given by the Cayley graphs of cocompact lattices in compactly generated groups. As an application, we show that a compactly generated group has polynomial growth if and only if its rough Cayley graph has polynomial growth (same for intermediate and exponential growth). Moreover, a unimodular compactly generated group is amenable if and only if its rough Cayley graph is amenable as a metric space.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا