ArticleOriginal scientific text
Title
Quantum classifying spaces and universal quantum characteristic classes
Authors 1
Affiliations
- Instituto de Matematicas, UNAM, Area de la Investigacion Cientifica, Circuito Exterior, Ciudad Universitaria, México DF, CP 04510, Mexico
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.
Bibliography
- A. Connes, Noncommutative Geometry, Academic Press (1994).
- S. Doplicher, J. E. Roberts, Endomorphisms of C*-algebras, Cross Products and Duality for Compact Groups, Ann Math, 130, 75-119 (1989).
- M. Đurđević, Geometry of Quantum Principal Bundles I, Commun Math Phys 175 (3) 457-521 (1996).
- M. Đurđević, Geometry of Quantum Principal Bundles II-Extended Version, Preprint, Instituto de Matematicas, UNAM, México (1994).
- M. Đurđević, Characteristic Classes of Quantum Principal Bundles, Preprint, Instituto de Matematicas, UNAM, México (1995).
- M. Đurđević, Quantum Principal Bundles and Their Characteristic Classes, this volume, 303-313.
- M. Đurđević, Geometry of Quantum Classifying Spaces, in preparation (1997).
- M. Đurđević, Cyclic Homology for Quantum Classifying Spaces, in preparation (1997).
- J.-L. Loday, Cyclic Homology, A series of Comprehensive Studies in Mathematics 301, Springer-Verlag (1992).
- S. L. Woronowicz, Compact Matrix Pseudogroups, Commun Math Phys 111 613-665 (1987).
- S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups/Quantum Groups, Commun Math Phys 122 125-170 (1989).