Spaces of maps into classifying spaces for equivariant crossed complexes, II: The general topological group case. Abstract The results of a previous paper [3] on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of homotopy coherence theory for cross...

Loop variables are used to describe the presence of topological defects in spacetime. In particular we study the dependence of the holonomy transformation on angular momentum and torsion for a multi-chiral cone. We also compute the holonomies for multiple moving crossed cosmic strings and two plane topological defects-crossed by a cosmic string. June/95 ∗ This work was supported in part by Cons...

We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov pro...

For an operator bimodule X over von Neumann algebras A ⊆ B(H) and B ⊆ B(K), the space of all completely bounded A, B-bimodule maps from X into B(K,H), is the bimodule dual of X. Basic duality theory is developed with a particular attention to the Haagerup tensor product over von Neumann algebras. To X a normal operator bimodule Xn is associated so that completely bounded A, B-bimodule maps from...

The universal properties of $$(2+1)$$ D topological phases matter enriched by a symmetry group G are described G-crossed extensions unitary modular tensor categories (UMTCs). While the fusion and braiding quasiparticles associated with order UMTC, further capture action, fractionalization, defects arising from interplay order. We describe relation between UMTC state spaces on general surfaces t...