منابع مشابه
Groups Which Act Pseudofreely on S 2 × S 2.
Recall that a pseudofree group action on a space is one whose singular set consists only of isolated points. In this paper, we classify all of the finite groups which admit pseudofree actions on S × S. The groups are exactly those which admit orthogonal pseudofree actions on S×S ⊂ R×R, and they are explicitly listed. This paper can be viewed as a companion to a paper of Edmonds [6], which unifo...
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Let Γ be a finitely generated, amenable group. Using an idea ofÉ. Ghys, we prove that if Γ has a nontrivial, orientation-preserving action on the real line, then Γ has an infinite, cyclic quotient. (The converse is obvious.) This implies that if Γ has a faithful action on the circle, then some finite-index subgroup of Γ has the property that all of its nontrivial, finitely generated subgroups h...
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We show that the group G∞ of germs at infinity of orientation-preserving homeomorphisms of R admits no action on the line. This gives an example of a left-orderable group of the same cardinality as Homeo+(R) that does not embed in Homeo+(R). As an application of our techniques, we construct a finitely generated group Γ ⊂ G∞ that does not extend to Homeo+(R) and, separately, extend a theorem of ...
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For those who know about group cohomology will know that if a group acts freely on sphere, then it has periodic cohomology. Now the group Zp×Zp does not have periodic cohomology, (just use the Künneth formula again) therefore it cannot act freely on any sphere. For those who do not know about group cohomology a finite group having periodic cohomology is equivalent to all the abelian subgroups b...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2007
ISSN: 0030-8730
DOI: 10.2140/pjm.2007.230.381