| Global Analysis on Foliated Spaces Softcover Repri Edition Contributor(s): Moore, Calvin C. (Author), Schochet, Claude (Author) |
|
 |
ISBN: 1461395941 ISBN-13: 9781461395942 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: December 2011 |
| Additional Information |
| BISAC Categories: - Computers | Programming Languages - General - Mathematics | Topology - General - Science | Physics - Mathematical & Computational |
| Dewey: 514.2 |
| Series: Mathematical Sciences Research Institute Publications |
| Physical Information: 0.72" H x 6.14" W x 9.21" (1.07 lbs) 337 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: Global analysis has as its primary focus the interplay between the local analysis and the global geometry and topology of a manifold. This is seen classicallv in the Gauss-Bonnet theorem and its generalizations. which culminate in the Ativah-Singer Index Theorem ASI] which places constraints on the solutions of elliptic systems of partial differential equations in terms of the Fredholm index of the associated elliptic operator and characteristic differential forms which are related to global topologie al properties of the manifold. The Ativah-Singer Index Theorem has been generalized in several directions. notably by Atiyah-Singer to an index theorem for families AS4]. The typical setting here is given by a family of elliptic operators (Pb) on the total space of a fibre bundle P = F_M_B. where is defined the Hilbert space on Pb 2 L 1p -llbl.dvollFll. In this case there is an abstract index class indlPI E ROIBI. Once the problem is properly formulated it turns out that no further deep analvtic information is needed in order to identify the class. These theorems and their equivariant counterparts have been enormously useful in topology. geometry. physics. and in representation theory. |