We show how general principles of symmetry in quantum mechanics lead to twisted notions
of a group representation. This framework generalizes both the classical threefold way of …

We construct a prequantum 2-Hilbert space for any line bundle gerbe whose Dixmier–
Douady class is torsion. Analogously to usual prequantization, this 2-Hilbert space has the …

To set the scene, we begin here by reviewing basics of homotopy theory via model category
theory [Quillen (1967)](review in [Hovey (1999)][Hirschhorn (2003)][Lurie (2009a), A. 2]) and …

We introduce an axiomatic framework for the parallel transport of connections on gerbes. It
incorporates parallel transport along curves and along surfaces, and is formulated in terms …

In this book we prove (Thm. 4. 3.24) unified classification results for stable equivariant Γ-
principal bundles when the underlying homotopy type SΓ of the topological structure group Γ …

We extend the Chern character on K-theory, in its generalization to the Chern-Dold
character on generalized cohomology theories, further to (twisted, differential) non-abelian …

In superstring theory spin structures are present on both the 2-dimensional worldsheet and
10-dimensional spacetime. We present a new proposal for the B-field in superstring theory …

We study (pre-) sheaves in bicategories on geometric categories: smooth manifolds,
manifolds with a Lie group action and Lie groupoids. We present three main results: we …

We present mathematical details of the construction of a topological invariant for periodically
driven two-dimensional lattice systems with time-reversal symmetry and quasienergy gaps …

In this book we prove unified classification results for equivariant principal bundles when the
topological structure group is truncated. The conceptually transparent proof invokes a …