E-theory for Lp algebras and the dual novikov conjecture
Institution: | Vanderbilt University |
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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/ |
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.