Topological properties of spaces of projective unitary representations

  title={Topological properties of spaces of projective unitary representations},
  author={Jesus F. Espinoza and Bernardo Uribe},
  journal={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
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


Parametrized homotopy theory
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
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
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
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
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
© Bulletin de la S. M. F., 1963, tous droits réservés. L’accès aux archives de la revue « Bulletin de la S. M. F. » (http://smf. implique l’accordExpand
Equivariant Homotopy and Cohomology Theory
Vektorraumbündel und der Raum der Fredholm-Operatoren
Topology, Second Edition
  • PrenticeHall, Inc., Englewood Cliffs, N.J.
  • 2000
Parametrized homotopy theory, volume 132 of Mathematical Surveys and Monographs
  • American Mathematical Society, Providence, RI.
  • 2006