Download Global Analysis on Foliated Spaces (Mathematical Sciences by Calvin C. Moore,Claude L. Schochet PDF

By Calvin C. Moore,Claude L. Schochet

Foliated areas glance in the community like items, yet their international constitution is mostly now not a product, and tangential differential operators are correspondingly extra complicated. within the Nineteen Eighties, Alain Connes based what's referred to now as noncommutative geometry and topology. one of many first effects used to be his generalization of the Atiyah-Singer index theorem to compute the analytic index linked to a tangential (pseudo) - differential operator and an invariant transverse degree on a foliated manifold, by way of topological info at the manifold and the operator. This moment variation provides an entire facts of this gorgeous outcome, generalized to foliated areas (not simply manifolds). It contains the required history from research, geometry, and topology. the current version has more desirable exposition, an up-to-date bibliography, an index, and extra fabric protecting advancements and purposes because the first version got here out, together with the affirmation of the distance Labeling Conjecture of Jean Bellissard.

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