论文标题
关于$ \ mathbb r^n $ action的轨道的最小尺寸
On the minimal dimension of the orbits of a $\mathbb R^n$-action
论文作者
论文摘要
考虑在连接的歧管$ m $上，不一定是$ m $的$ \ mathbb r^n $的平稳动作，尺寸$ m $和等级$ k $。假设$ m $不是气缸。然后存在尺寸$ <（m+k）/2 $的动作的轨道。结果，一个人表明，如果有$ m $ 4 \ ell \ geq 4 $的pontrjagin类的非零元素，则存在dimension $ \ leq m- \ ell-1 $的轨道。
Consider a smooth action of $\mathbb R^n$ on a connected manifold $M$, not necessarily compact, of dimension $m$ and rank $k$. Assume that $M$ is not a cylinder. Then there exists an orbit of the action of dimension $<(m+k)/2$. As a consequence, one shows that if there is a non-zero element of the ring of Pontrjagin classes of $M$ of degree $4\ell\geq 4$, then there exists an orbit of the action of dimension $\leq m-\ell-1$.
