C*-algebras and Elliptic Theory II - 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 C*-algebras and Elliptic Theory II write by Dan Burghelea. This book was released on 2008-03-18. C*-algebras and Elliptic Theory II available in PDF, EPUB and Kindle. This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. The topics covered include the index of operators, torsion invariants, K-theory of operator algebras and L2-invariants. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.
C*-algebras and Elliptic Theory
C*-algebras and Elliptic 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 C*-algebras and Elliptic Theory write by Bogdan Bojarski. This book was released on 2006-11-09. C*-algebras and Elliptic Theory available in PDF, EPUB and Kindle. This book consists of reviewed original research papers and expository articles in index theory (especially on singular manifolds), topology of manifolds, operator and equivariant K-theory, Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others, and applications in mathematical physics. The wide spectrum of subjects reflects the diverse directions of research for which the starting point was the Atiyah-Singer index theorem.
The Localization Problem in Index Theory of Elliptic Operators
The Localization Problem in Index Theory of Elliptic Operators - 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 The Localization Problem in Index Theory of Elliptic Operators write by Vladimir Nazaikinskii. This book was released on 2013-11-26. The Localization Problem in Index Theory of Elliptic Operators available in PDF, EPUB and Kindle. The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.
C * -Algebras and Elliptic Operators in Differential Topology
C * -Algebras and Elliptic Operators in Differential 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 C * -Algebras and Elliptic Operators in Differential Topology write by I_U_ri_ Petrovich Solov_v Evgeni_ Vadimovich Troit_s_ki_. This book was released on 2000-10-03. C * -Algebras and Elliptic Operators in Differential Topology available in PDF, EPUB and Kindle. The aim of this book is to present some applications of functional analysis and the theory of differential operators to the investigation of topological invariants of manifolds. The main topological application discussed in the book concerns the problem of the description of homotopy-invariant rational Pontryagin numbers of non-simply connected manifolds and the Novikov conjecture of homotopy invariance of higher signatures. The definition of higher signatures and the formulation of the Novikov conjecture are given in Chapter 3. In this chapter, the authors also give an overview of different approaches to the proof of the Novikov conjecture. First, there is the Mishchenko symmetric signature and the generalized Hirzebruch formulae and the Mishchenko theorem of homotopy invariance of higher signatures for manifolds whose fundamental groups have a classifying space, being a complete Riemannian non-positive curvature manifold. Then the authors present Solovyov's proof of the Novikov conjecture for manifolds with fundamental group isomorphic to a discrete subgroup of a linear algebraic group over a local field, based on the notion of the Bruhat-Tits building. Finally, the authors discuss the approach due to Kasparov based on the operator $KK$-theory and another proof of the Mishchenko theorem. In Chapter 4, they outline the approach to the Novikov conjecture due to Connes and Moscovici involving cyclic homology. That allows one to prove the conjecture in the case when the fundamental group is a (Gromov) hyperbolic group. The text provides a concise exposition of some topics from functional analysis (for instance, $C^*$-Hilbert modules, $K$-theory or $C^*$-bundles, Hermitian $K$-theory, Fredholm representations, $KK$-theory, and functional integration) from the theory of differential operators (pseudodifferential calculus and Sobolev chains over $C^*$-algebras), and from differential topology (characteristic classes). The book explains basic ideas of the subject and can serve as a course text for an introduction to the study of original works and special monographs.
Theory
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 Theory write by Steven Lord. This book was released on 2021-07-19. Theory available in PDF, EPUB and Kindle. This book is the second edition of the first complete study and monograph dedicated to singular traces. The text offers, due to the contributions of Albrecht Pietsch and Nigel Kalton, a complete theory of traces and their spectral properties on ideals of compact operators on a separable Hilbert space. The second edition has been updated on the fundamental approach provided by Albrecht Pietsch. For mathematical physicists and other users of Connes’ noncommutative geometry the text offers a complete reference to traces on weak trace class operators, including Dixmier traces and associated formulas involving residues of spectral zeta functions and asymptotics of partition functions.
