Noé Bárcenas

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. 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.

Stable finiteness properties of infinite discrete groups

Let

Topological rigidity of higher graph manifolds

G

SEGAL'S SPECTRAL SEQUENCE IN TWISTED EQUIVARIANT K-THEORY FOR PROPER AND DISCRETE ACTIONS

be an infinite discrete group. A classifying space for proper actions of

Twisted equivariant K- Theory and K-Homology of Sl3(Z)

G

Positive scalar curvature and low-degree group homology

is a proper

Multiplicative structures and the twisted Baum-Connes assembly map

G

Twisted Geometric K-homology for Proper actions of discrete groups

-CW-complex

The Completion Theorem in twisted equivariant

X

K

such that the fixed point sets