Global Analysis On Foliated Spaces
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Global Analysis on Foliated Spaces
Author: Calvin C. Moore
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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.
Global Analysis on Foliated Spaces
This book presents a complete proof of Connes' Index Theorem generalized to foliated spaces, including coverage of new developments and applications.
Commutative Algebra and Noncommutative Algebraic Geometry
Author: David Eisenbud
language: en
Publisher: Cambridge University Press
Release Date: 2015-11-19
This book surveys fundamental current topics in these two areas of research, emphasising the lively interaction between them. Volume 2 focuses on the most recent research.