Category
page 1Fiber bundles
fiber bundle
continuous surjection satisfying a local triviality condition
covering space
type of continuous map in topology
principal bundle
fiber bundle whose fibers are group torsors (groups with the identity element forgotten)
Hopf fibration
fiber bundle of the 3-sphere over the 2-sphere, with 1-spheres as fibers
Villarceau circles
Shape produced by intersection of a torus

section
right inverse of a fiber bundle map
connection form
math/physics concept
frame bundle
principal bundle associated to a vector bundle, whose fiber is the (torsor over the) automorphism group of the vector-bundle fiber
Seifert fiber space
circle bundle over a 2 dimensional orbifold
classifying space
topological space equipped with a principal bundle with the property that any principal bundle (with the same fiber group) over a paracompact manifold is isomorphic to a pullback of the principal bundle over this topological space
parallelizable manifold
a differentiable manifold whose (co)tangent bundle is topologically trivial
principal bundle connection
Ehresmann connection on a principal bundle that is compatible with the group action
associated bundle
fiber bundle constructed by a representation of a group and a principal bundle
bundle
generalization of a fiber bundle dropping the condition of a local product structure
circle bundle
fiber bundle whose fibers are circles
Stiefel manifold
the manifold of all orthonormal k-frames in n-dimensional Euclidean space
pullback bundle
fiber bundle induced by a map of its base space