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Index theory (Mathematics) --- Price indexes

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Index theory studies the solutions to differential equations on geometric spaces, their relation to the underlying geometry and topology, and applications to physics. If the space of solutions is infinite dimensional, it becomes necessary to generalise the classical Fredholm index using tools from the K-theory of operator algebras. This leads to higher index theory, a rapidly developing subject with connections to noncommutative geometry, large-scale geometry, manifold topology and geometry, and operator algebras. Aimed at geometers, topologists and operator algebraists, this book takes a friendly and concrete approach to this exciting theory, focusing on the main conjectures in the area and their applications outside of it. A well-balanced combination of detailed introductory material (with exercises), cutting-edge developments and references to the wider literature make this a valuable guide to this active area for graduate students and experts alike.

Index theory (Mathematics) --- C*-algebras. --- K-theory.

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Analytic functions --- Fredholm operators --- Index theory (Mathematics) --- Von Neumann algebras

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Index theory (Mathematics) --- Geometry, Differential. --- Topology. --- Singularities (Mathematics) --- Geometry [Differential ] --- Congresses

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The Novikov Conjecture is the single most important unsolved problem in the topology of high-dimensional non-simply connected manifolds. These two volumes are the outgrowth of a conference held at the Mathematisches Forschungsinstitut Oberwolfach (Germany) in September 1993, on the subject of 'Novikov Conjectures, Index Theorems and Rigidity'. They are intended to give a snapshot of the status of work on the Novikov Conjecture and related topics from many points of view: geometric topology, homotopy theory, algebra, geometry and analysis. Volume 1 contains: • A detailed historical survey and bibliography of the Novikov Conjecture and of related subsequent developments, including an annotated reprint (both in the original Russian and in English translation) of Novikov's original 1970 statement of his conjecture; • An annotated problem list; • The texts of several important unpublished classic papers by Milnor, Browder, and Kasparov; and • Research/survey papers on the Novikov Conjecture by Ferry/Weinberger, Gromov, Mishchenko, Quinn, Ranicki, and Rosenberg.

Index theorems --- Novikov conjecture --- Conjecture, Novikov --- Novikov's conjecture --- Manifolds (Mathematics) --- Differential operators --- Global analysis (Mathematics) --- Index theory (Mathematics) --- Rigidity (Geometry) --- Congresses. --- Novikov conjecture - Congresses. --- Index theorems - Congresses.