Homogeneous vector bundles on homogeneous spaces
Homogeneous vector bundles on homogeneous spaces
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齐次空间上的齐次向量丛
DOI：
10.1016/0040-9383(72)90007-9
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发表时间：
1972
期刊：
影响因子：
--
通讯作者：
H. Pittie
中科院分区：
文献类型：
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作者：
H. Pittie
本文的目的是解决Atiyah-Hirzebruch[2]关于某些齐性空间的复K-理论的一个猜想。具体地说，设G是一个紧的连通李群，x，（G）是自由的，设U是一个最大秩的闭连通子群;那么U的复表示给出G/U上的齐次复向量丛，猜想是映射2：R（U）-+ K”（G/U）是满射的，实际上我们的贡献是代数性质的（定理1和定理2）由此猜想，如霍奇金[5]指出。事实上，这项工作是刺激了试图提供失踪环节霍奇金计划。V. Snaith和R.西摩
THE PURPOSE of this note is to settle a conjecture of Atiyah-Hirzebruch[2] on the complex K-theory of certain homogeneous spaces. Specifically, let G be a compact, connected lie group with x,(G) free, and let U be a closed connected subgroup of maximal rank; then complex representations of U give homogeneous, complex vector-bundles on G/U, and the conjecture is that the map 2: R (U)--+ K”(G/U) so induced is surjective.Actually our contribution is of an algebraic nature (Theorems 1 and 2 below) from which the conjecture follows, as Hodgkin [5] has pointed out. In fact this work was stimulated by an attempt to supply the missing link in Hodgkin’s scheme. Independent proofs along similar lines have been given by V. Snaith and R. Seymour.