Quantum Classifying Spaces and Universal Quantum Characteristic Classes

Abstract

A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical concept of the classifying map is introduced and analyzed. Interrelations with the abstract algebraic theory of quantum characteristic classes are discussed. Various non-equivalent approaches to defining universal characteristic classes are outlined.

12 pages, AMS-LaTeX, Lectures, Quantum Groups and Quantum Spaces Minisemester, Banach Center, Warsaw, Poland, November 1995