回想一下，空间上的伪自由群作用是其奇异集仅由孤立点组成的作用。本文对S^2 × S^2上所有允许伪自由作用的有限群进行了分类。这些群恰好是我们所期望的群：它们允许S^2 x S^2上的正交伪自由作用作为R^3 x R^3的子集。它们被明确列出。这篇论文可以被看作是Edmonds，math.GT/9809055论文的姊妹篇。
英文摘要：
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^2 x S^2. The groups turn out to be exactly the expected ones: those which admit orthogonal pseudofree actions on S^2 x S^2 as a subset of R^3 x R^3. They are explicitly listed.
This paper can be viewed as a companion to a paper of Edmonds, math.GT/9809055.
R. S. Kulkarni表明，一个有限群的作用伪自由，但不自由，保持方向，在一个偶数维领域（或适当的球形空间）要么是一个周期群半自由地与两个不动点，一个二面体群与三个奇异轨道，或一个多面体群，只发生在2维。本文证明了当n全等于0 mod 4时，二面体群在实际n-球面上不是伪自由的和局部线性的作用。当n等于2 mod 4且n>2时，这种作用的可能性仍然是开放的。还考虑了方向反转动作。
There are four groups $G$ fitting into a short exact sequence $ 1\rightarrow SL(2,5)\rightarrow G\rightarrow C_2\rightarrow 1, $ where $SL(2,5)$ is the special linear group of $(2\times 2)$-matrices with entries in the field of five elements. Except for the direct product of $SL(2,5)$ and $C_2$, there are two other semidirect products of these two groups and just one non-semidirect product $SL(2,5).C_2$, considered in this paper. It is known that each finite nonsolvable group can act on spheres with arbitrary positive number of fixed points. Clearly, $SL(2,5).C_2$ is a nonsolvable group. Moreo…
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The action dimension of a discrete group $G$ is the minimum dimension of contractible manifold that admits a proper $G$-action. We compute the action dimension of the direct limit of a simple complex of groups for several classes of examples including: 1) Artin groups, 2) graph products of groups, and 3) fundamental groups of aspherical complements of arrangements of affine hyperplanes.
A classical result by K.B. Lee states that every group morphism between almost crystallographic groups is induced by an affine map on the nilpotent Lie group whereon these groups by definition act. It is the main technique for studying morphisms between virtually nilpotent groups, having important applications in fixed point theory, for example as a tool to compute Nielsen numbers for self-maps on infra-nilmanifolds. In this paper we generalize this result to morphisms between virtually polycyclic groups, which are known to act crystallographically by affine transformations on a nilpotent Lie …
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