Universal twist in equivariant K‐theory for proper and discrete actions. Issue 5 (22nd November 2013)

• Record Type: Journal Article
• Authors: Bárcenas, Noé; Espinoza, Jesús; Joachim, Michael; Uribe, Bernardo
• Is Part Of: Proceedings of the London Mathematical Society. Volume 108:Issue 5(2014:May)
• Page Start: 1313
• Page End: 1350
• Publication Date: 2013-11-22
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms/pdt061
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract : 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. We construct universal equivariant projective unitary stable bundles for the orbit types, and we use a specific model for these local universal spaces in order to glue them to obtain a universal equivariant projective unitary stable bundle for discrete and proper actions. We determine the homotopy type of the universal equivariant projective unitary stable bundle, and we show that the isomorphism classes of equivariant projective unitary stable bundles are classified by the third equivariant integral cohomology group. The results contained in this paper extend and generalize results of Atiyah–Segal.