Global Analysis on Foliated Spaces

Moore, Calvin C.; Schochet, Claude L.

ISBN 10: 1461395941 / ISBN 13: 9781461395942

Edité par Springer-Verlag New York Inc., 2011

A propos de cet article

Series: Mathematical Sciences Research Institute Publications. Num Pages: 337 pages, biography. BIC Classification: PBPD; PHU. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 18. Weight in Grams: 527. . 2011. Softcover reprint of the original 1st ed. 1988. Paperback. . . . .

N° de réf. du vendeur V9781461395942

Détails bibliographiques

• Titre: Global Analysis on Foliated Spaces
• Éditeur: Springer-Verlag New York Inc.
• Date de parution: 2011
• Langue: anglais
• ISBN à 10 chiffres: 1461395941
• ISBN à 13 chiffres: 9781461395942
• Reliure: Couverture souple
• État de l'article: New

A propos de ce titre

Synopsis

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.