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The 2-Hilbert Space of a Prequantum Bundle Gerbe
We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier-Douady class is torsion. Analogously to usual prequantisation, this 2-Hilbert space has the category of sections ofExpand
Geometry and 2-Hilbert space for nonassociative magnetic translations
We suggest a geometric approach to quantisation of the twisted Poisson structure underlying the dynamics of charged particles in fields of generic smooth distributions of magnetic charge, and duallyExpand
Fluxes, bundle gerbes and 2-Hilbert spaces
We elaborate on the construction of a prequantum 2-Hilbert space from a bundle gerbe over a 2-plectic manifold, providing the first steps in a programme of higher geometric quantisation of closedExpand
Categorical structures on bundle gerbes and higher geometric prequantisation
We present a construction of a 2-Hilbert space of sections of a bundle gerbe, a suitable candidate for a prequantum 2-Hilbert space in higher geometric quantisation. We introduce a direct sum on theExpand
Smooth 2-Group Extensions and Symmetries of Bundle Gerbes
We study bundle gerbes on manifolds $M$ that carry an action of a connected Lie group $G$. We show that these data give rise to a smooth 2-group extension of $G$ by the smooth 2-group of hermiteanExpand
Sheaves of Higher Categories and Presentations of Smooth Field Theories
We study the extension of higher presheaves on a category $C$ to its free cocompletion $\hat{C}$. Here, higher presheaves take values in $\infty$-categories of $(\infty,n)$-categories, for any $n \inExpand
Transgression of D-branes
Closed strings can be seen either as one-dimensional objects in a target space or as points in the free loop space. Correspondingly, a B-field can be seen either as a connection on a gerbe over theExpand
Gerbes in Geometry, Field Theory, and Quantisation
Abstract This is a mostly self-contained survey article about bundle gerbes and some of their recent applications in geometry, field theory, and quantisation. We cover the definition of bundle gerbesExpand
Instantons on conical half-flat 6-manifolds
A bstractWe present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones overExpand
Topological insulators and the Kane–Mele invariant: Obstruction and localization theory
We present homotopy theoretic and geometric interpretations of the Kane-Mele invariant for gapped fermionic quantum systems in three dimensions with time-reversal symmetry. We show that the invariantExpand