(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
An $n$-vector bundle is an fiber ∞-bundle whose fibers are n-vector spaces of sorts.
For $\mathbf{B}U(1)$ the circle 2-group and $2 Vect$ the category of 2-vector spaces (objects are categories equivalence to $A$ Mod for some associative algebra or algebroid $A$, morphisms are bimodules) there is a canonical 1-dimensional ∞-representation?
on the 1-dimensional 2-vector space $Vect_{\mathcal{C}}$.
For $g : X \to \mathbf{B}^2 U(1)$ a cocycle for a circle 2-bundle, the composite
is the corresponding classifying map for the “associated line 2-bundle”.
A section of $\rho(g)$ is a twisted vector bundle with twist given by $\rho$.
principal bundle / torsor / groupoid principal bundle / associated bundle
(∞,1)-vector bundle / $(\infty,n)$-vector bundle
Last revised on December 12, 2012 at 17:08:43. See the history of this page for a list of all contributions to it.