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https://hdl.handle.net/2440/28890
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 |
Publisher: | TOHOKU UNIVERSITY |
Issue Date: | 2001 |
Conference Name: | Pacific Rim Geometry Conference (5th : 2000 : Sendai, Japan) |
Editor: | Seiki Nishikawa, |
Statement of Responsibility: | 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. |
Appears in Collections: | Aurora harvest 2 Pure Mathematics publications |
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