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 ...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.展开更多
文摘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.
