K-Theories for Certain Infinite Rank Bundles

Details K-Theories for Certain Infinite Rank Bundles K-Theories for Certain Infinite Rank Bundles

2011-07-24

arxiv.org/abs/1107.4811v1

Mathematics

K-Theory and Homology

Scientific paper

Several authors have recently constructed characteristic classes for classes of infinite rank vector bundles appearing in topology and physics. These include the tangent bundle to the space of maps between closed manifolds, the infinite rank bundles in the families index theorem, and bundles with pseudodifferential operators as structure group. In this paper, we construct the corresponding K-theories for these types of bundles. We develop the formalism of these theories and use their Chern character to detect a large class of nontrivial elements.

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