Index Theory for Locally Compact Noncommutative Geometries - 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 for Locally Compact Noncommutative Geometries write by A. L. Carey. This book was released on 2014-08-12. Index Theory for Locally Compact Noncommutative Geometries available in PDF, EPUB and Kindle. Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.
From Differential Geometry to Non-commutative Geometry and Topology
From Differential Geometry to Non-commutative Geometry and Topology - 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 From Differential Geometry to Non-commutative Geometry and Topology write by Neculai S. Teleman. This book was released on 2019-11-10. From Differential Geometry to Non-commutative Geometry and Topology available in PDF, EPUB and Kindle. This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
Noncommutative Geometry
Noncommutative Geometry - 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 Noncommutative Geometry write by Alain Connes. This book was released on 2003-12-15. Noncommutative Geometry available in PDF, EPUB and Kindle. Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Index Theory Beyond the Fredholm Case
Index Theory Beyond the Fredholm Case - 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 Beyond the Fredholm Case write by Alan Carey. This book was released on 2022-11-30. Index Theory Beyond the Fredholm Case available in PDF, EPUB and Kindle. This book is about extending index theory to some examples where non-Fredholm operators arise. It focuses on one aspect of the problem of what replaces the notion of spectral flow and the Fredholm index when the operators in question have zero in their essential spectrum. Most work in this topic stems from the so-called Witten index that is discussed at length here. The new direction described in these notes is the introduction of `spectral flow beyond the Fredholm case'. Creating a coherent picture of numerous investigations and scattered notions of the past 50 years, this work carefully introduces spectral flow, the Witten index and the spectral shift function and describes their relationship. After the introduction, Chapter 2 carefully reviews Double Operator Integrals, Chapter 3 describes the class of so-called p-relative trace class perturbations, followed by the construction of Krein's spectral shift function in Chapter 4. Chapter 5 reviews the analytic approach to spectral flow, culminating in Chapter 6 in the main abstract result of the book, namely the so-called principal trace formula. Chapter 7 completes the work with illustrations of the main results using explicit computations on two examples: the Dirac operator in Rd, and a differential operator on an interval. Throughout, attention is paid to the history of the subject and earlier references are provided accordingly. The book is aimed at experts in index theory as well as newcomers to the field.
An Introduction to C*-Algebras and Noncommutative Geometry
An Introduction to C*-Algebras and Noncommutative Geometry - 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 An Introduction to C*-Algebras and Noncommutative Geometry write by Heath Emerson. This book was released on . An Introduction to C*-Algebras and Noncommutative Geometry available in PDF, EPUB and Kindle.
