AbstractsMathematics

E-theory for Lp algebras and the dual novikov conjecture

by Fan Fei Chong




Institution: Vanderbilt University
Department: Mathematics
Degree: PhD
Year: 2014
Keywords: Non-commutative Geometry; K-theory
Record ID: 2029752
Full text PDF: http://etd.library.vanderbilt.edu/available/etd-06052014-203201/


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.