Band 9
Global Analysis on Foliated Spaces
Aus der Reihe
Mathematical Sciences Research Institute Publications
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- Taschenbuch ausgewählt
- eBook
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Sprache:Englisch
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Verlag:Springer Us
Fr. 72.90
inkl. gesetzl. MwSt.,
Beschreibung
Produktdetails
Einband
Taschenbuch
Erscheinungsdatum
14.12.2011
Verlag
Springer UsSeitenzahl
337
Maße (L/B/H)
23.5/15.5/1.9 cm
Gewicht
528 g
Auflage
Softcover reprint of the original 1st ed. 1988
Sprache
Englisch
ISBN
978-1-4613-9594-2
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.
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