E-theory for Lp algebras and the dual novikov conjecture

Abstract

Generalizing E-theory for C*-algebras of A. Connes and N. Higson, we defined E-theory for Lp algebras - a bivariant K-theory for closed algebra of bounded linear operators on some Lp(µ) space. We showed that our theory has product, Bott Periodicity, six-term exact sequence in both variables for σ-unital extensions and Mayer-Viertoris exact sequence. We formulated and proved Dual lp Novikov Conjecture for discrete torsion-free groups which admit isometric and metrically proper action on a lp Banach space.