等变Borsuk-Ulam定理  

The Equivariant Borsuk Ulams Theorem

作　　者：张志强[1] 

机构地区：[1]兰州大学数学系

出　　处：《兰州大学学报（自然科学版）》1999年第2期7-11,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金;甘肃省自然科学基金

摘　　要：在紧致李群双作用下的Ｂａｎａｃｈ空间中，讨论了非等价等变严格集压缩场的拓扑度计算问题．提出并利用等变子方法和作用子方法，通过等变Ｓａｒｄ－Ｓｍａｌｅ定理和单作用等变拓扑度定理，取消了现有结论对紧致李群的交换性假设和群表示形式的特殊性要求，还取消了现有结论对作用空间的有限维限制。In the Banach spaces (X,T) and (X,S) acted by the compact Lie group G , the calculation of the mapping degree of G equivariant strict set contraction field f∈C 1(Ω,X) is discussed with the following equivariant Borsuk Ulams Theorem as the main result. Let (X,T) and (X,S) be two non singular representation Banachs spaces of the compact Lie group G . If Ω is a ( G,T ) invariant bounded open set, f∈C 1(Ω,X) is a ( G,T,S ) equivariant strict set contraction field, and 0f(Ω) , then deg (f,Ω,0)=α[β deg (f| Fix G ,Ω∩ Fix G,0)+ni=1m iχ(N i)], where α,β are two constant numbers of the representations (G,T) and (G,S) , Fix G is the ( G,T ) fixed space, N 1,N 2,…,N n are some (G,T) orbits in Ω,χ is the Eulers characteristic .

关 键 词：紧致李群 等变子 巴拿赫空间 B-U定理 

分 类 号：O177.91[理学—数学]