GLOBAL ANALYSIS ON FOLIATED SPACES

Moore, Calvin C. and Claude Schochet

ISBN 10: 0387966641 / ISBN 13: 9780387966649

Published by Springer-Verlag, New York, 1988

[viii], 337pp Mathematical Sciences Research Institute Publications 9 Size: 8vo - over 7¾" - 9¾" tall. Seller Inventory # 010321

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.

Book Description: Foliated spaces look locally like products, but their global structure is generally not a product, and tangential differential operators are correspondingly more complex. In the 1980s, Alain Connes founded what is now known as noncommutative topology.This book presents a complete proof of Connes' Index Theorem, generalized to foliated spaces (not just manifolds). It includes the necessary background from analysis, geometry, and topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering developments and applications since the first edition came out.

Bibliographic Details

Title: GLOBAL ANALYSIS ON FOLIATED SPACES
Publisher: Springer-Verlag, New York
Publication Date: 1988
Binding: Hard Cover
Condition: Very Good
Dust Jacket Condition: No Jacket
Edition: First Printing.