nLab bundles - contents

bundles

• (stable) parameterized homotopy theory

• fiber bundles in physics

• Chern-Weil theory

Context

• slice topos, slice (∞,1)-topos

• (linear) dependent type theory

Classes of bundles

• covering space

• retractive space

• fiber bundle, fiber ∞-bundle

  numerable bundle

  • sphere bundle

  • projective bundle

• principal bundle, principal ∞-bundle

  • principal 2-bundle, principal 3-bundle

  • circle bundle, circle n-bundle

  • orientation bundle

  • spinor bundle, stringor bundle

• associated bundle, associated ∞-bundle

  • gerbe, 2-gerbe, ∞-gerbe,

  • local coefficient bundle

• vector bundle, 2-vector bundle, (∞,1)-vector bundle

  real, complex/holomorphic, quaternionic

  topological, differentiable, algebraic

  with connection

  • line bundle

    complex, holomorphic, algebraic

    cubical structure

  • Chern-Weil theory

  • topological K-theory

  • tensor categoryof vector bundles

    (VectBund)

  • direct sum, tensor product, external tensor product, inner product

  • dual vector bundle

  • stable vector bundle

  • virtual vector bundle

• bundle of spectra

• natural bundle

• equivariant bundle

Universal bundles

• universal principal bundle, universal principal ∞-bundle

• universal vector bundle, universal complex line bundle

• subobject classifier, object classifier

Presentations

• bundle gerbe

• groupal model for universal principal ∞-bundles

• microbundle

Examples

• empty bundle, zero bundle

• trivial vector bundle

• tangent bundle, normal bundle

• tautological line bundle

  • basic line bundle on the 2-sphere

• Hopf fibration

• canonical line bundle

• prequantum circle bundle, prequantum circle n-bundle

Constructions

• clutching construction