论文标题
歧管的模棱两可的嵌入到欧几里得空间中
Equivariant embeddings of manifolds into Euclidean spaces
论文作者
论文摘要
假设有限的$ g $在歧管$ m $上表现出来。由Mostow的定理（也是宫殿），有一个$ g $ equivariant的嵌入 $ m $ in $ m $ dimensional Euclidean Space $ \ rr^{m} $对于某些$ M $。我们对这种$ M $的某些明确范围感兴趣。 首先，我们提供上限：存在$ g $ equivariant的嵌入 $ m $ in $ \ rr^{d | g | +1} $，其中$ | g | $是$ g $的订单，$ g $和$ m $嵌入到$ \ rr^d $中。 接下来，我们为有限循环组动作$ g $提供一个下限 $ g $ equivariant嵌入 $ m $ in $ \ rr^{m} $，然后$ m \ ge 2l $。 给出了一些对表面的应用。
Suppose a finite group $G$ acts on a manifold $M$. By a theorem of Mostow, also Palais, there is a $G$-equivariant embedding of $M$ into the $m$-dimensional Euclidean space $\RR^{m}$ for some $m$. We are interested in some explicit bounds of such $m$. First we provide an upper bound: there exists a $G$-equivariant embedding of $M$ into $\RR^{d|G|+1}$, where $|G|$ is the order of $G$ and $M$ embeds into $\RR^d$. Next we provide a lower bound for finite cyclic group action $G$: If there are $l$ points having pairwise co-prime lengths of $G$-orbits greater than $1$ and there is a $G$-equivariant embedding of $M$ into $\RR^{m}$, then $m\ge 2l$. Some applications to surfaces are given.
