Global Analysis on Foliated Spaces

Calvin C. Moore, Claude Schochet (Autoren)

Buch | Softcover

337 Seiten

2011 | Softcover reprint of the original 1st ed. 1988
Springer-Verlag New York Inc.
978-1-4613-9594-2 (ISBN)

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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.

I. Locally Traceable Operators.- II. Foliated Spaces.- III. Tangential Cohomology.- IV. Transverse Measures.- V. Characteristic Classes.- VI. Operator Algebras.- VII. Pseudodifferential Operators.- VIII. The Index Theorem.- Appendices.- C: Positive Scalar Curvature Along the Leaves.- References.

Reihe/Serie	Mathematical Sciences Research Institute Publications ; 9
Zusatzinfo	VII, 337 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Themenwelt	Naturwissenschaften ► Physik / Astronomie
ISBN-10	1-4613-9594-1 / 1461395941
ISBN-13	978-1-4613-9594-2 / 9781461395942
Zustand	Neuware