Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments.
However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium.
Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

Inhalt

Preface. Methods of Equivariant Quantization; C. Dubal, et al. Application of Noncommutative Differential Geometry on Lattice to Anomaly Analysis in Abelian Lattice Gauge Theory; T. Fujiwara, et al. Geometrical Structures on Noncommutative Spaces; O. Grandjean. A Relation Between Commutative and Noncommutative Descriptions of D-Branes; N. Ishibashi. Intersection Numbers on the Moduli Spaces of Stable Maps in Genus 0; A. Kabanov, T. Kimura. D-Brane Actions on Kähler Manifolds; A. Kato. On the Projective Classification of the Modules of Differential Operators on Rm; P.B.A. Lecomte. An Interpretation of Schouten-Nijenhuis Bracket; K. Mikami. Remarks on the Characteristic Classes Associated with the Group of Fourier Integral Operators; N. Miyazaki. C*-Algebraic Deformation and Index Theory; T. Natsume. Singular Systems of Exponential Functions; H. Omori, et al. Determinants of Elliptic Boundary Problems in Quantum Field Theory; S.G. Scott, et al. On Geometry of Non-Abelian Duality; P. Severa. Weyl Calculus and Wigner Transform on the Poincaré Disk; T. Tate. Lectures on Graded Differential Algebras and Noncommutative Geometry; M. Dubois-Violette.