(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
geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
The concept of line n-bundle in complex analytic geometry, classified by maps into the $n$-fold delooping $\mathbf{B}^n \mathbb{G}_m$ of the multiplicative group.
for $n = 0$ these are holomorphic functions classified by the group of units;
for $n= 1$ these are holomorphic line bundles, classified by Picard group, modulated by Picard stack;
for $n =2$ these are holomorphic line 2-bundles, classified by Brauer group, modulated by Brauer stack
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Last revised on July 15, 2014 at 05:07:06. See the history of this page for a list of all contributions to it.