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Frame bundle
About: Frame bundle is a research topic. Over the lifetime, 1600 publications have been published within this topic receiving 23049 citations.
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TL;DR: In this paper, a geometric theory for bundle shifts and its duality to the geometric theory of Cowen-Douglas operators is proposed. But this theory is not applicable to the case of Hilbert space operators.
6 citations
TL;DR: In this article, the relation between the dynamics on the base space of a vector bundle and that on each associated bundle of frames is discussed and a continuation of a previous one is presented.
Abstract: This paper is a continuation of a previous one. We still emphasize the discussion on the relation between the dynamics on the base space of a vector bundle and that on each associated bundle of frames.
6 citations
6 citations
TL;DR: In this paper, an explicit Cech cocycle representing the k-th Stiefel-Whitney class of a vector bundle is constructed, which involves only the transition functions of the bundle.
Abstract: We construct an explicit Cech cocycle representing the k-th Stiefel-Whitney class of a vector bundle. This construction involves only the transition functions of the bundle. We also give local formulae for the secondary Stiefel-Whitney classes. These may be useful in determining whether the Stiefel-Whitney numbers of a flat bundle are zero.
6 citations
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TL;DR: In this paper, a spinor bundle is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product over a compact connected orientable smooth manifold with Riemannian metric.
Abstract: A bundle gerbe is constructed from an oriented smooth vector bundle of even rank with a fiberwise inner product, over a compact connected orientable smooth manifold with Riemannian metric. From a trivialization of the bundle gerbe is constructed an irreducible Clifford module bundle, a spinor bundle over the smooth free loop space of the manifold.
First, a Clifford algebra bundle over the loop space is constructed from the vector bundle. A polarization class bundle is constructed, choosing continuously over each point of the loop space a polarization class of Lagrangian subspaces of the complexification of the real vector space from which the Clifford algebra is made. Being unable to choose a Lagrangian subspace continuously from the polarization class over each point, the thesis constructs a bundle gerbe over the loop space of the base manifold to encode over each loop all such subspaces, along with the isomorphisms between the Fock spaces made from them, resulting from their being in the same polarization class.
The vanishing of the Dixmier-Douady class of the bundle gerbe implies that the latter has a trivialization, from which is constructed a spinor bundle.
6 citations