# Topological properties of spaces of projective unitary representations

@article{Espinoza2015TopologicalPO,
title={Topological properties of spaces of projective unitary representations},
author={Jesus F. Espinoza and Bernardo Uribe},
journal={arXiv: Algebraic Topology},
year={2015}
}
• Published 20 November 2015
• Physics, Mathematics
• arXiv: Algebraic Topology
Let $G$ be a compact and connected Lie group and $PU(\mathcal H)$ be the group of projective unitary operators on a separable Hilbert space $\mathcal H$ endowed with the strong operator topology. We study the space $hom_{st}(G, PU(\mathcal H))$ of continuous homomorphisms from $G$ to $PU(\mathcal H)$ which are stable, namely the homomorphisms whose induced representation contains each irreducible representation an infinitely number of times. We show that the connected components of $hom_{st}(G… Expand 2 Citations Twisted geometric K-homology for proper actions of discrete groups We define Twisted Equivariant [Formula: see text]-homology groups using geometric cycles. We compare them with analytical approaches using Kasparov KK-theory and (twisted) [Formula: seeExpand On adiabatic cycles of quantum spin systems Motivated by the Ω-spectrum proposal of unique gapped ground states by Kitaev [1], we study adiabatic cycles in gapped quantum spin systems from various perspectives. We give a few exactly solvableExpand #### References SHOWING 1-10 OF 17 REFERENCES Parametrized homotopy theory • Mathematics • 2006 Prologue Point-set topology, change functors, and proper actions: Introduction to Part I The point-set topology of parametrized spaces Change functors and compatibility relations Proper actions,Expand Twisted K-theory • Mathematics • 2004 Twisted complex K-theory can be defined for a space X equipped with a bundle of complex projective spaces, or, equivalently, with a bundle of C ∗ -algebras. Up to equivalence, the twistingExpand Universal twist in Equivariant K-theory for proper and discrete actions • Mathematics • 2012 We define equivariant projective unitary stable bundles as the appropriate twists when defining K-theory as sections of bundles with fibers the space of Fredholm operators over a Hilbert space. WeExpand Topological properties of the unitary group • Mathematics • 2014 We show that the strong operator topology, the weak operator topology and the compact-open topology agree on the space of unitary operators of a infinite dimensional separable Hilbert space.Expand Equivariant principal bundles and their classifying spaces • Mathematics • 2014 We consider \Gamma-equivariant principal G-bundles over proper \Gamma-CW-complexes with prescribed family of local representations. We construct and analyze their classifying spaces for locallyExpand Champs continus d’espaces hilbertiens et de$C^\ast \$ -algèbres
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