Differential orbifold \(K\)-theory. (English) Zbl 1327.19012
Summary: We construct differential \(K\)-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct a push-forward map in differential orbifold K-theory. Finally, we construct a non-degenerate intersection pairing with values in \(\mathbb{C}/\mathbb{Z}\) for the subclass of smooth orbifolds which can be written as global quotients by a finite group action. We construct a real subfunctor of our theory, where the pairing restricts to a non-degenerate \(\mathbb{R}/\mathbb{Z}\)-valued pairing.
MSC:
19L50 | Twisted \(K\)-theory; differential \(K\)-theory |
58J20 | Index theory and related fixed-point theorems on manifolds |
58J28 | Eta-invariants, Chern-Simons invariants |
19L47 | Equivariant \(K\)-theory |
19K56 | Index theory |
58J35 | Heat and other parabolic equation methods for PDEs on manifolds |
Keywords:
differential \(K\)-theory; equivariant differential \(K\)-theory; orbifold; push-forward in differential \(K\)-theory; localization in equivariant differential \(K\)-theoryReferences:
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