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As he nears death he calls them to him and gives them an object lesson in the need for unity. Having bound a bundle of sticks together (or in other accounts either spears or arrows), he asks his sons to break them. When they fail, he undoes the bundle and either breaks each stick singly or gets his sons to do so.
A faggot, in the meaning of "bundle", is an archaic English unit applied to bundles of certain items. Alternate spellings in Early Modern English include fagate, faget, fagett, faggott, fagot, fagatt, fagott, ffagott, and faggat. A similar term is found in other languages (e.g. Latin: fascis).
One example of a principal bundle is the frame bundle. If for each two points b 1 and b 2 in the base, the corresponding fibers p −1 (b 1) and p −1 (b 2) are vector spaces of the same dimension, then the bundle is a vector bundle if the appropriate conditions of local triviality are satisfied. The tangent bundle is an example of a vector ...
A "bundle of sticks" – in which each stick represents an individual right – is a common analogy made for the bundle of rights. Any property owner possesses a set of "sticks" related directly to the land. [5] For example, perfection of a mechanic's lien takes some, but not all, rights out of the bundle held by the owner. Extinguishing that ...
In this way, the connection form can be used to define the horizontal bundle: The horizontal bundle is the kernel of the connection form. The solder form or tautological one-form vanishes on the vertical bundle and is non-zero only on the horizontal bundle. By definition, the solder form takes its values entirely in the horizontal bundle.
From any vector bundle, one can construct the frame bundle of bases, which is a principal bundle (see below). Another special class of fiber bundles, called principal bundles , are bundles on whose fibers a free and transitive action by a group G {\displaystyle G} is given, so that each fiber is a principal homogeneous space .
In algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point. Smoothness is one way of making precise the notion of a scheme with no singular points. A special case is the notion of a smooth variety over a field. Smooth schemes play the role in algebraic geometry of manifolds in topology.
where is a connection on a principal bundle , is a section of an associated spinor bundle and / is the induced Dirac operator of the induced covariant derivative on this associated bundle. The first term is an interacting term in the Lagrangian between the spinor field (the field representing the electron-positron) and the gauge field ...