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...
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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 کاملHyperbolic Structures on 3-manifolds, Ii: Surface Groups and 3-manifolds Which Fiber over the Circle
The main result (0.1) of this paper is that every atoroidal three-manifold that fibers over the circle has a hyperbolic structure. Consequently, every fibered three-manifold admits a geometric decomposition. The main tool for constructing hyperbolic structures on fibered three-manifolds is the double limit theorem (4.1), which is of interest for its own sake and lays out general conditions unde...
متن کاملMost Rank Two Finite Groups Act Freely on a Homotopy Product of Two Spheres
A classic result of Swan states that a finite group G acts freely on a finite homotopy sphere if and only if every abelian subgroup of G is cyclic. Following this result, Benson and Carlson conjectured that a finite group G acts freely on a finite complex with the homotopy type of n spheres if the rank of G is less than or equal to n. Recently, Adem and Smith have shown that every rank two fini...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1975
ISSN: 0386-2194
DOI: 10.3792/pja/1195518668