Search results
Results From The WOW.Com Content Network
Vector bundle morphisms are a special case of the notion of a bundle map between fiber bundles, and are sometimes called (vector) bundle homomorphisms. A bundle homomorphism from E 1 to E 2 with an inverse which is also a bundle homomorphism (from E 2 to E 1) is called a (vector) bundle isomorphism, and then E 1 and E 2 are said to be ...
If E is a complex vector bundle, then the conjugate bundle ¯ of E is obtained by having complex numbers acting through the complex conjugates of the numbers. Thus, the identity map of the underlying real vector bundles: ¯ = is conjugate-linear, and E and its conjugate E are isomorphic as real vector bundles.
Pages in category "Vector bundles" The following 55 pages are in this category, out of 55 total. This list may not reflect recent changes. ...
A vector bundle together with an orientation is called an oriented bundle. A vector bundle that can be given an orientation is called an orientable vector bundle. The basic invariant of an oriented bundle is the Euler class. The multiplication (that is, cup product) by the Euler class of an oriented bundle gives rise to a Gysin sequence.
The dual of a complex vector bundle is indeed isomorphic to the conjugate bundle ¯, but the choice of isomorphism is non-canonical unless is equipped with a hermitian product. The Hom bundle H o m ( E 1 , E 2 ) {\displaystyle \mathrm {Hom} (E_{1},E_{2})} of two vector bundles is canonically isomorphic to the tensor product bundle E 1 ∗ ⊗ E ...
A common example of a principal bundle is the frame bundle of a vector bundle, which consists of all ordered bases of the vector space attached to each point. The group G , {\displaystyle G,} in this case, is the general linear group , which acts on the right in the usual way : by changes of basis .
A double vector bundle consists of (,,,), where . the side bundles and are vector bundles over the base ,; is a vector bundle on both side bundles and ,; the projection, the addition, the scalar multiplication and the zero map on E for both vector bundle structures are morphisms.
Vertical and horizontal subspaces for the Möbius strip. The Möbius strip is a line bundle over the circle, and the circle can be pictured as the middle ring of the strip. . At each point on the strip, the projection map projects it towards the middle ring, and the fiber is perpendicular to the middle ri