nLab
line n-bundle

Idea

For $\mathbb{G}_m$ the multiplicative group, a $\mathbf{B}^{n-1}\mathbb{G}_m$ principal infinity-bundle, modulated by a cocycle $X\to \mathbf{B}^n \mathbb{G}_m$, classified by a cohomology class in in $H^n(X,\mathbb{G}_m)$.

Examples

• universal Chern-Simons line 3-bundle

Related concepts

• line bundle

• line 2-bundle

• circle n-bundle with connection

• holomorphic line n-bundle

moduli spaces of line n-bundles with connection on $n$-dimensional $X$

$n$	Calabi-Yau n-fold	line n-bundle	moduli of line n-bundles	moduli of flat/degree-0 n-bundles	Artin-Mazur formal group of deformation moduli of line n-bundles	complex oriented cohomology theory	modular functor/self-dual higher gauge theory of higher dimensional Chern-Simons theory
$n = 0$		unit in structure sheaf	multiplicative group/group of units		formal multiplicative group	complex K-theory
$n = 1$	elliptic curve	line bundle	Picard group/Picard scheme	Jacobian	formal Picard group	elliptic cohomology	3d Chern-Simons theory/WZW model
$n = 2$	K3 surface	line 2-bundle	Brauer group	intermediate Jacobian	formal Brauer group	K3 cohomology
$n = 3$	Calabi-Yau 3-fold	line 3-bundle		intermediate Jacobian		CY3 cohomology	7d Chern-Simons theory/M5-brane
$n$				intermediate Jacobian