The purpose of this monograph is to give an analytic proof of an index formula for the relative de Rham cohomology groups which may be considered as a generalization of the celebrated Hodge-Kodaira theory for the absolute de Rham cohomology groups. More precisely, let X be a compact oriented smooth Riemannian manifold without boundary, and Y a submanifold of X. The purpose is to find an operator D such that ind D = X(X) - X(Y) where X(X) and X(Y) are the Euler-Poincare characteristics of X and Y, respectively. The crucial ...
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The purpose of this monograph is to give an analytic proof of an index formula for the relative de Rham cohomology groups which may be considered as a generalization of the celebrated Hodge-Kodaira theory for the absolute de Rham cohomology groups. More precisely, let X be a compact oriented smooth Riemannian manifold without boundary, and Y a submanifold of X. The purpose is to find an operator D such that ind D = X(X) - X(Y) where X(X) and X(Y) are the Euler-Poincare characteristics of X and Y, respectively. The crucial point is how to introduce spaces of currents on X and Y in which the index formula for D holds. In deriving this index formula, the theory of harmonic forms satisfying an interior boundary condition plays a fundamental role. The approach here has a great advantage of intuitive interpretation of the index formula in terms of Brownian motion from the point of view of probability theory, and the result may be stated as follows: Brownian motion describes the topology of a compact Riemannian manifold through its Euler-Poincare characteristic.
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Add this copy of Brownian Motion and Index Formulas for the De Rham to cart. $120.00, good condition, Sold by HaroldsBooks rated 5.0 out of 5 stars, ships from Corydon, IA, UNITED STATES, published 1998 by Wiley-VCH.
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Good/No Jacket. 3527401393 Ex-Library Ex-library with the usual features. The interior is clean and tight. Binding and cover are good. The book has been rebound in a good hard cover. 215 pages.
