Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 42, No. 2, pp. 547-555 (2001)

On the Permutation Products of Manifolds

Samet Kera

Institute of Mathematics, P.O.Box 162, 1000 Skopje, Macedonia, e-mail:

Abstract: In this paper it is proven the following conjecture: If $G$ is a subgroup of the permutation group $S_{n}$ and $M$ is a 2-dimensional real manifold, then $M^{n}/G$ is a manifold if and only if $G=S_{m_{1}}\times S_{m_{2}}\times \cdots \times S_{m_{r}}$ where $S_{m_{1}},\ldots ,S_{m_{r}}$ are permutation groups of partition of $\{1,2,\ldots ,n\}$ into $r$ subsets with cardinalities $m_{1},\ldots ,m_{r}$, and $M^n$ is the topological product of $n$ copies of $M$.

Keywords: permutation products on manifolds, cyclic products on manifolds, permutation group

Classification (MSC2000): 53C99, 20B35

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