Higher Index Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Higher Index Theory write by Rufus Willett. This book was released on 2020-07-02. Higher Index Theory available in PDF, EPUB and Kindle. 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, Coarse Geometry, and Topology of Manifolds
Index Theory, Coarse Geometry, and Topology of Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Index Theory, Coarse Geometry, and Topology of Manifolds write by John Roe. This book was released on 1996. Index Theory, Coarse Geometry, and Topology of Manifolds available in PDF, EPUB and Kindle. Lecture notes from the conference held Aug. 1995 in Boulder, Colo.
Higher Topos Theory
Higher Topos Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Higher Topos Theory write by Jacob Lurie. This book was released on 2009-07-26. Higher Topos Theory available in PDF, EPUB and Kindle. In 'Higher Topos Theory', Jacob Lurie presents the foundations of this theory using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
Index Theory with Applications to Mathematics and Physics
Index Theory with Applications to Mathematics and Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Index Theory with Applications to Mathematics and Physics write by David Bleecker. This book was released on 2013. Index Theory with Applications to Mathematics and Physics available in PDF, EPUB and Kindle. Describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. David Bleecker and Bernhelm Boo�-Bavnbek give two proofs of the Atiyah-Singer Index Theorem in impressive detail: one based on K-theory and the other on the heat kernel approach.
Analytic K-Homology
Analytic K-Homology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analytic K-Homology write by Nigel Higson. This book was released on 2000-12-07. Analytic K-Homology available in PDF, EPUB and Kindle. Analytic K-homology draws together ideas from algebraic topology, functional analysis and geometry. It is a tool - a means of conveying information among these three subjects - and it has been used with specacular success to discover remarkable theorems across a wide span of mathematics. The purpose of this book is to acquaint the reader with the essential ideas of analytic K-homology and develop some of its applications. It includes a detailed introduction to the necessary functional analysis, followed by an exploration of the connections between K-homology and operator theory, coarse geometry, index theory, and assembly maps, including a detailed treatment of the Atiyah-Singer Index Theorem. Beginning with the rudiments of C* - algebra theory, the book will lead the reader to some central notions of contemporary research in geometric functional analysis. Much of the material included here has never previously appeared in book form.
