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Type: Conference paper
Title: On positivity of the Kadison constant and noncommutative Bloch theory
Author: Varghese, M.
Citation: Proceedings of the Fifth Pacific Rim Geometry Conference / pp. 107-124
Issue Date: 2001
Conference Name: Pacific Rim Geometry Conference (5th : 2000 : Sendai, Japan)
Editor: Seiki Nishikawa,
Statement of
Varghese Mathai
Abstract: In [V. Mathai, K-theory of twisted group C*-algebras and positive scalar curvature, Contemp. Math. 231 (1999) 203–225], we established a natural connection between the Baum-Connes conjecture and noncommutative Bloch theory, viz., the spectral theory of projectively periodic elliptic operators on covering spaces. We elaborate on this connection here and provide significant evidence for a fundamental conjecture in noncommutative Bloch theory on the non-existence of Cantor set type spectrum. This is accomplished by establishing an explicit lower bound for the Kadison constant of twisted group C*-algebras in a large number of cases, whenever the multiplier is rational.
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