The present work grew out of a study of the Maslov class (e. g. (37]), which is a fundamental invariant in asymptotic analysis of partial differential equations of quantum physics. One of the many inยญ terpretations of this class was given by F. Kamber and Ph. Tondeur (43], and it indicates that the Maslov class is a secondary characteristic class of a complex trivial vector bundle endowed with a real reduction of its structure group. (In the basic paper of V. I. Arnold about the Maslov class (2], it is also pointed out without details that the Maslov class is characteristic in the category of vector bundles mentioned preยญ viously. ) Accordingly, we wanted to study the whole range of secondary characteristic classes involved in this interpretation, and we gave a short description of the results in (83]. It turned out that a complete exposition of this theory was rather lengthy, and, moreover, I felt that many potential readers would have to use a lot of scattered references in order to find the necessary information from either symplectic geometry or the theory of the secondary characteristic classes. On the otherhand, both these subjects are of a much larger interest in differential geomeยญ try and topology, and in the applications to physical theories
SUBJECT
Mathematics
Partial differential equations
Geometry
Manifolds (Mathematics)
Complex manifolds
Physics
Quantum physics
Mechanics
Mathematics
Geometry
Mathematical Methods in Physics
Partial Differential Equations
Manifolds and Cell Complexes (incl. Diff.Topology)
