The Aityah-Singer index theorem is a powerful tool for relating geometry, analysis, and topology. In its original form, however, it applies only to compact manifolds. This study describes a version of index which works for noncompact spaces with appropriate control, such as complete Riemannian manifolds. The relevant control is provided by the large scale geometry of the space, and basic notions of large scale geometry are developed. Index theory for the signature operator is related to geometric topology via surgery theory ...
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The Aityah-Singer index theorem is a powerful tool for relating geometry, analysis, and topology. In its original form, however, it applies only to compact manifolds. This study describes a version of index which works for noncompact spaces with appropriate control, such as complete Riemannian manifolds. The relevant control is provided by the large scale geometry of the space, and basic notions of large scale geometry are developed. Index theory for the signature operator is related to geometric topology via surgery theory. And, paralleling the analytic development, controlled surgery theories for noncompact spaces have been developed by topologists. This explores the connections between these theories, producing a natural transformation from surgery to analytic surgery. The analytic foundations of the work come from the theory of C*-algebras, and the properties of the C*-algebra of a coarse space are developed in some detail. The book is based on lectures presented at a conference held in Boulder, Colorado, in August 1995 and includes the author's notes and descriptions of some constructions that were finalized after the lectures were delivered.
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Add this copy of Index Theory, Coarse Geometry, and Topology of to cart. $22.92, very good condition, Sold by Zubal Books rated 4.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 1996 by American Mathematical Society.
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Add this copy of Index Theory, Coarse Geometry, and Topology of to cart. $63.22, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1996 by American Mathematical Society.
