(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
The generalization of a $G$-principal ∞-bundle over an ∞-group $G$ as $G$ is generalized to a groupoid object in an (∞,1)-category.
For $\mathbf{H}$ an (∞,1)-topos and $\mathcal{G}_\bullet \in Grp_\infty(\mathbf{H})$ a groupoid object in an (∞,1)-category, a $\mathcal{G}_\bullet$-principal $\infty$-bundle over $X$ is
a morphism $P \to X$
equipped with an anchor $a \colon P \to \mathcal{G}_0$ and a groupoid ∞-action of $\mathcal{G}_\bullet$ on $(P,a)$ over $X$;
such that $P \to X \simeq (P//\mathcal{G})$ is the corresponding quotient map.
Last revised on January 5, 2018 at 05:12:53. See the history of this page for a list of all contributions to it.