52449

Автор(ов):

2

Параметры публикации

Глава в книге

Название:

Monge–Ampère Grassmannians, Characteristic Classes and All That

Сведения об издании:

Monge–Ampère Grassmannians, Characteristic Classes and All That

ISBN/ISSN:

978-3-030-17030-1

DOI:

10.1007/978-3-030-17031-8

Наименование источника:

• Nonlinear PDEs, Their Geometry, and Applications

• Basel

Издательство:

• Springer Nature

2019

Страницы:

233-257
Аннотация
It is known (since Maslov observations) that the analogues of Bohr–Sommerfeld conditions in the asymptotic quantisation (know also as the Maslov’s canonical operator method) have a topological nature. This condition has a form of annihilation of some cohomology classes (the Maslov–Arnold classes). The Maslov–Arnold classes are, in fact, the examples of characteristic classes, which are completely defined by a universal construction of a ‘classifying map’ into a ‘classifying space’ phase space T∗M. The topology of this Lagrangian Grassmannian and its Z2−cohomology ring H∗ (LG,Z2) are well known (A. Borel, D. Fuchs). The classes of Maslov–Arnold contain an important information about singularities for the Lagrangian projections. In this paper, we review and describe one of the generalizations of Maslov–Arnold classes associated with a topological study of Monge–Ampère equations and their solutions. This important tool for studies of Monge–Ampère solution singularities

Библиографическая ссылка:

Лычагин В.В., Roubtsov V.N. Monge–Ampère Grassmannians, Characteristic Classes and All That / Nonlinear PDEs, Their Geometry, and Applications. Basel: Springer Nature, 2019. С. 233-257.