Advances in partial differential equations: elliptic theory and noncommutative geometry

The book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorophisms of the manifold on which the operators are defined. The main goal of the study is to relate analytical invariants (in particular, the index) of such operators to topological invariants of the manifold itself. This problem can be solved by modern methods of noncommutative geometry. To make the book self-contained, the authors have included necessary geometric material (C*-algebras and their K-theory, cyclic homology, etc.). First and so far the only book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators Provides important results, which are in a sense definitive, on the above-mentioned topic and at the same time contains all the necessary preliminary material, thus being effectively self-contained Not only comprehensive but rather concise, making it even more attractive for readers at any level Can serve as a concise introduction to noncommutative geometry, which is one of the most powerful tools for studying a wide rangeof problems in mathematics and theoretical physics

• ISBN: 978-3-7643-8774-7
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 240
• Fecha Publicación: 01/06/2008
• Nº Volúmenes: 1
• Idioma: Inglés