A Thom isomorphism for infinite rank Euclidean bundles
A Thom isomorphism for infinite rank Euclidean bundles
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无限阶欧几里德丛的 Thom 同构
DOI：
10.4310/hha.2003.v5.n1.a7
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
J. Trout
中科院分区：
文献类型：
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作者：
J. Trout
对于有限维黎曼流形上的无限阶欧几里德向量束，给出并证明了算子k理论中的一个等变Thom同构定理。这个论证的主要成分是构造一个非交换的C ？-与束E相关的代数！M，具有相容连接r，它在无限维总空间e上起函数代数的作用。如果基M是一个点，我们得到无限维欧几里德空间的Higson-Kasparov-Trout[19]的Bott周期同构定理。对偶维自旋c -流形上偶有限秩自旋c -束的构造简化为拓扑k理论中的经典Thom同构。这些技术涉及非交换几何泛函分析。
An equivariant Thom isomorphism theorem in operator Ktheory is formulated and proven for infinite rank Euclidean vector bundles over finite dimensional Riemannian manifolds. The main ingredient in the argument is the construction of a non-commutative C ? -algebra associated to a bundle E ! M, equipped with a compatible connection r, which plays the role of the algebra of functions on the infinite dimensional total space E. If the base M is a point, we obtain the Bott periodicity isomorphism theorem of Higson-Kasparov-Trout [19] for infinite dimensional Euclidean spaces. The construction applied to an even finite rank spin c -bundle over an even-dimensional proper spin c -manifold reduces to the classical Thom isomorphism in topological K-theory. The techniques involve noncommutative geometric functional analysis.