منابع مشابه
Which Finite Groups Act Freely on Spheres?
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...
متن کاملPartially Ordered Groups Which Act on Oriented Order Trees
It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of left-invariant partial orders on groups which yield such actions, and show c...
متن کاملGroups 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...
متن کاملCompact Lie Groups Which Act on Euclidean Space without Fixed Points
It is shown that a compact Lie group G with identity component Gq acts without fixed points on euclidean space if and only if G„ is nonabelian or G/G0 is not of prime power order, which completes earlier work of P. E. Conner and E. E. Floyd, Conner and D. Montgomery, and W.C. Hsiang and W.-Y. Hsiang. In this note we describe completely the class of compact Lie groups which can act without fixed...
متن کاملWhich 3-manifold Groups Are Kähler Groups?
The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if G is both a (closed) 3-manifold group and a Kähler group, then G must be finite.
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ژورنال
عنوان ژورنال: Ergodic Theory and Dynamical Systems
سال: 1983
ISSN: 0143-3857,1469-4417
DOI: 10.1017/s0143385700001917