Asymptotic and Fredholm representations of discrete groups

Abstract

We consider generalised Scherk Schwarz reductions of supergravity and superstring theories with twists by electromagnetic dualities that are symmetries of the equations of motion but not of the action, such as the S-duality of D = 4, N = 4 super-Yang-Mills coupled to supergravity. The reduction cannot be done on the action itself, but must be done either on the field equations or on a duality invariant form of the action, such as one in the doubled formalism in which potentials are introduced for both electric and magnetic fields. The resulting theory in odd-dimensions has massive form fields satisfying a self-duality condition dA ∼ m * A. We construct such theories in D = 3, 5, 7.

Asymptotic homomorphisms into the Calkin algebra

“…A useful tool for working with asymptotic homomorphisms is the possibility of discretization suggested by Mishchenko [13], [10], [11]. A sequence of maps…”

“…In [10], [11], [12] a natural map E : ½½A; B n K ! ExtðSA; BÞ was constructed and it was proved that the composition CH E is an isomorphism whenever A is a suspension.…”

“…0 for i f n: where E is the map constructed in [10], [11], and from the similar equality CH E ¼ Bott 2 [10], [11]. r…”

OnC*-algebras related to asymptotic homomorphisms

“…Proposition 2.4 ( [3]) For any κ one has K 0 (Q(κ)) = Z and K 1 (Q(κ)) = 0. K 0 (Q(κ)) is generated by the sequence (e 1 , e 1 , e 1 , .…”

Almost-representations and asymptotic representations of discrete groups

“…Remember that in [9] a map R asym (Γ)−→K 0 (BΓ) (10) was constructed, which factorizes [8] through the assembly map…”