| 1. | This principal-bundle is the associated bundle of the M�bius strip.
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| 2. | See Ehresmann connection # Associated bundles for more details.
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| 3. | The companion concept to associated bundles is the "'reduction of the structure group "'of a G-bundle B.
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| 4. | Cartan connections induce covariant derivatives and other differential operators on certain associated bundles, hence a notion of parallel transport.
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| 5. | We first introduce the general procedure for producing an associated bundle, with specified fibre, from a given fibre bundle.
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| 6. | Since " ? " is a principal connection, it induces a connection on any associated bundle to " Q ".
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| 7. | The firm's lobbyist and his associates bundled contributions amounting to $ 20, 000 for McCain's presidential campaign, all perfectly legal.
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| 8. | The tangent bundle TX of a world manifold X and the associated bundle atlas of finite number of trivialization charts.
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| 9. | In other words, we ask to identify the image of the associated bundle mapping ( which is actually a functor ).
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| 10. | It gives rise to ( Ehresmann ) connections on any fiber bundle associated to " P " via the associated bundle construction.
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