Estimates of the Isovariant Borsuk–Ulam Constants of Connected Compact Lie Groups  

作　　者：Ikumitsu NAGASAKI 

机构地区：[1]Department of Mathematics,Kyoto Prefectural University of Medicine

出　　处：《Acta Mathematica Sinica,English Series》2018年第10期1485-1500,共16页数学学报（英文版）

摘　　要：The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.

关 键 词：Isovariant map Borsuk-Ulam type theorem Borsuk Ulam constant transformation groups representation theory 

分 类 号：O152.5[理学—数学]