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Dale Husemöller (also spelled Husemoller) is an American mathematician specializing in algebraic topology and homological algebra who is known for his books on fibre bundles, elliptic curves, and, in collaboration with John Milnor, symmetric bilinear forms.
Download as PDF; Printable version ... of a manifold and related structures such as vector bundles and other fiber bundles. ... Husemoller, D (1994), Fibre bundles, ...
It is an affine bundle modelled on the vector bundle VP/G → M whose typical fiber is the Lie algebra g of structure group G, and where G acts on by the adjoint representation. There is the canonical imbedding of C to the quotient bundle T P / G which also is called the bundle of principal connections .
A G-bundle is a fiber bundle with an equivalence class of G-atlases. The group G is called the structure group of the bundle; the analogous term in physics is gauge group. In the smooth category, a G-bundle is a smooth fiber bundle where G is a Lie group and the corresponding action on F is smooth and the transition functions are all smooth maps.
Conversely, general bundle maps can be reduced to bundle maps over a fixed base space using the notion of a pullback bundle. If π F:F→ N is a fiber bundle over N and f:M→ N is a continuous map, then the pullback of F by f is a fiber bundle f * F over M whose fiber over x is given by (f * F) x = F f(x).
This line bundle L is the Möbius strip (which is a fiber bundle whose fibers can be equipped with vector space structures in such a way that it becomes a vector bundle). The cohomology group H 1 ( S 1 ; Z / 2 Z ) {\displaystyle H^{1}(S^{1};\mathbb {Z} /2\mathbb {Z} )} has just one element other than 0.
The first definition of fiber space is given by Hassler Whitney in 1935 under the name sphere space, but in 1940 Whitney changed the name to sphere bundle. [ 3 ] [ 4 ] The theory of fibered spaces, of which vector bundles , principal bundles , topological fibrations and fibered manifolds are a special case, is attributed to Seifert , Hopf ...
In mathematics, a bundle is a generalization of a fiber bundle dropping the condition of a local product structure. The requirement of a local product structure rests on the bundle having a topology. Without this requirement, more general objects can be considered bundles. For example, one can consider a bundle π: E → B with E and B sets.