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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, it was shown that on an arbitrary oriented Lorentzian six-manifold, there is always an Sp2 twist that allows such spinors to be defined globally.
Abstract: Fermion fields on an M-theory five-brane carry a representation of the double cover of the structure group of the normal bundle. It is shown that, on an arbitrary oriented Lorentzian six-manifold, there is always an Sp2 twist that allows such spinors to be defined globally. The vanishing of the arising potential obstructions does not depend on spin structure in the bulk, nor does the six-manifold need to be spin or spin. Lifting the tangent bundle to such a generalised spin bundle requires picking a generalised spin structure in terms of certain elements in the integral and modulo-two cohomology of the five-brane world-volume in degrees four and five, respectively.
3 citations
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TL;DR: In this paper, the authors studied the stability of the normal bundle of canonical genus $8$ curves and proved that on a general curve the bundle is stable, based on Mukai's description of these curves as linear sections of a Grassmannian.
Abstract: We study the stability of the normal bundle of canonical genus $8$ curves and prove that on a general curve the bundle is stable. The proof rests on Mukai's description of these curves as linear sections of a Grassmannian $\mathrm{G}(2,6)$. This is the next case of a conjecture by M. Aprodu, G. Farkas, and A. Ortega: the general canonical curve of every genus $g \geq 7$ should have stable normal bundle. We also give some more evidence for this conjecture in higher genus.
3 citations
TL;DR: In this paper, the stable unextendibility of vector bundles over the quatemionic projective space Hpn was studied by making use of combinatorial properties of the Stiefel-Whitney classes and the Pontrjagin classes.
Abstract: We study the stable unextendibility of vector bundles over the quatemionic projective space Hpn by making use of combinatorial properties of the Stiefel-Whitney classes and the Pontrjagin classes. First, we show that the tangent bundle of Hpn is not stably extendible to Hpn+1 for n ~ 2, and also induce such a result for the normal bundle associated to an immersion of Hpn into R4n+k. Secondly, we show a sufficient condition for a quatemionic r-dimensional vector bundle over Hpn not to be stably extendible to Hpn+1 for r ::; n and I > 0, which is also a necessary condition when r = n and I = I.
3 citations
TL;DR: In this paper, the authors introduced a geometric interpretation of the quantum Knizhnik-Zamolodchikov equations introduced in 1991 by I.Frenkel and N.Reshetikhin, which can be linked to certain holomorphic vector bundles on the N-th Cartesian power of an elliptic curve.
Abstract: The paper introduces a new geometric interpretation of the quantum Knizhnik-Zamolodchikov equations introduced in 1991 by I.Frenkel and N.Reshetikhin. It turns out that these equations can be linked to certain holomorphic vector bundles on the N-th Cartesian power of an elliptic curve. These bundles are naturally constructed by a gluing procedure from a system of trigonometric quantum affine $R$-matrices. Meromorphic solutions of the quantum KZ equations are interpreted as sections of such a bundle. This interpretation is an analogue of the interpretation of solutions of the classical KZ equations as sections of a flat vector bundle. Matrix elements of intertwiners between representations of the quantum affine algebra correspond to regular (holomorphic) sections. The vector bundle obtained from the quantum KZ system is topologically nontrivial. Its topology can be completely described in terms of crystal bases, using the crystal limit ``q goes to 0''. In the case N=2, this bundle is is essentially a bundle on an elliptic curve which is shown to be semistable (for the case of quantum sl(2)) if the parameters take generic values. The proof makes use of the crystal limit ``q goes to 0''. Finally, we give a vector bundle interpretation of the generalized quantum KZ equations for arbitrary affine root systems defined recently by Cherednik.
3 citations
TL;DR: In this article, the authors studied natural lifting operations from a bundle τ : E → R to the bundle π : J 1 τ ∗ → E which is the dual of the first-jet bundle J 1τ.
3 citations