球面与紧致空间乘积的K理论  

K-theory for Product of Sphere and Compact Space

作　　者：唐九奇 崔婷婷 钟佳媚 TANG Jiu-qi;CUI Ting-ting;ZHONG Jia-mei(Guilin University of Science and Technology,Guilin 541000,Guangxi,China)

机构地区：[1]桂林学院理工学院,广西桂林541000

出　　处：《红河学院学报》2025年第2期132-133,140,共3页Journal of Honghe University

基　　金：广西高校中青年教师科研基础能力提升项目(2021KY1595)。

摘　　要：在拓扑K理论中,我们主要证明了如下结果:对任意紧致的Hausdorff空间X,存在以下同构,当n=2k(k≥0)时,K^(0)(X×S~n)≌K^(0)(x)十K^(0)(X);而当n=2k-1(k≥1)时,有K^(0)(X×S~n)≌K^(-1)(X)■K^(0)(X).当n=2k-1(k≥1)时,K^(0)(X×S~n)≌K^(-1)(X×S~n);而当n=2左(k≥0)时,K^(-1)(X×S~n)≌K^(-1)■K^(-1)(X).我们的结果依赖于以下两个事实:一是拓扑K理论中的博特周期定理和球面与欧式空间的一点紧致化同胚,这导致我们去算非紧空间作一点紧致化后的K理论;二是对任意局部紧的Hausdorff空间X总有K^(0)(X×R)≌K^(-1)(X)成立.最后,我们进一步推广了相关结论,算出环面的拓扑K理论.This paper discuses the following result in K-theory of topology,for any compact Hausdorff space,there exists the isomorphism,if n=2k(k≥0),K^(0)(X×Sn)=K^(0)(X)⊕K^(0)(X)and if n=2k-1(k≥1)⊕K^(0)(X×Sn)=K^(-1)(X)⊕K^(0)(X).Next,if n=2k-1(k≥1),K^(0)(X×Sn)=K^(-1)(X×Sn)and n=2k(k≥0),K^(-1)(X×Sn)=K^(-1)(X)⊕K^(-1)(X).The results depend on the following two facts:one is the Bott periodic theorem in topological theory and the homeomorphism of one-point compactification of spherical and Euclidic Spaces,which leads us to calculate the K-theory of one-point compactification of noncompact Spaces.The other the fact K^(0)(X×R)=K^(-1)(X)which is always true for any locally compact Hausdorff space.

关 键 词：紧致性 HAUSDORFF空间 拓扑K理论 

分 类 号：O189.2[理学—数学]