A Hilbert bundle description of differential K-theory
A Hilbert bundle description of differential K-theory
复制标题
DOI：
10.1016/j.aim.2018.02.002
复制
发表时间：
2015-12
期刊：
影响因子：
--
通讯作者：
A. Gorokhovsky;J. Lott
中科院分区：
文献类型：
--
作者：
A. Gorokhovsky;J. Lott
给出了流形M的微分K-理论的无穷维描述。生成元是三元组[H，A，ω]，其中H是M上的Z2-分次Hilbert丛，A是H上的超连通，ω是M上的微分形式.这些关系涉及eta形式。我们证明了紧接着的群是微分K-群K <$0（M）。此外，我们还构造了有限维上循环在适当浸没下的推进定理。给出奇微分K-群K <$1（M）的类似刻划.最后，我们给出了扭微分K-理论的一个模型。
We give an infinite dimensional description of the differential K-theory of a manifold M. The generators are triples [H, A, ω] where H is a Z 2-graded Hilbert bundle on M, A is a superconnection on H and ω is a differential form on M. The relations involve eta forms. We show that the ensuing group is the differential K-group K ˇ 0 (M). In addition, we construct the pushforward of a finite dimensional cocycle under a proper submersion with a Riemannian structure. We give the analogous description of the odd differential K-group K ˇ 1 (M). Finally, we give a model for twisted differential K-theory.