论文标题
Borsuk-小学Abelian 2组的Ulam定理
Borsuk--Ulam theorems for elementary abelian 2-groups
论文作者
论文摘要
让$ g $成为一个紧凑的谎言组，让$ u $和$ v $为有限维真实$ g $ - 模块，$ v^g = 0 $。 Marzantowicz，de Mattos和Dos Santos的一个定理估计，当$ u $ $ $ g $是$ u $ g $ $ g $ g $时，$ g $ map的零设置的范围是$ u $ g $的$ g $ g $，这是基本的基本Abelian $ p $ -p $ group，对于某些Prime P $或torus。在本说明中，经典的borsuk-紫外定理将用于对其结果进行改进，以估计零集的该部分的尺寸，而零集的该部分的尺寸是基础的Abelian $ p $ - group $ g $自由行动或用有限的同性恋组的torus $ g $ ACT。
Let $G$ be a compact Lie group and let $U$ and $V$ be finite-dimensional real $G$-modules with $V^G=0$. A theorem of Marzantowicz, de Mattos and dos Santos estimates the covering dimension of the zero-set of a $G$-map from the unit sphere in $U$ to $V$ when $G$ is an elementary elementary abelian $p$-group for some prime $p$ or a torus. In this note, the classical Borsuk--Ulam theorem will be used to give a refinement of their result estimating the dimension of that part of the zero-set on which an elementary abelian $p$-group $G$ acts freely or a torus $G$ acts with finite isotropy groups.
