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.
C*-algebras and Elliptic Theory II
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.
Elliptic Theory and Noncommutative Geometry
Elliptic Theory 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 Elliptic Theory and Noncommutative Geometry write by Vladimir E. Nazaykinskiy. This book was released on 2008-06-30. Elliptic Theory and Noncommutative Geometry available in PDF, EPUB and Kindle. This comprehensive yet concise book deals with nonlocal elliptic differential operators. These are operators whose coefficients involve shifts generated by diffeomorphisms of the manifold on which the operators are defined. This is the first book featuring a consistent application of methods of noncommutative geometry to the index problem in the theory of nonlocal elliptic operators. To make the book self-contained, the authors have included necessary geometric material.
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.
Index Theory of Elliptic Operators, Foliations, and Operator Algebras
Index Theory of Elliptic Operators, Foliations, and Operator Algebras - 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 of Elliptic Operators, Foliations, and Operator Algebras write by Jerome Kaminker. This book was released on 1988. Index Theory of Elliptic Operators, Foliations, and Operator Algebras available in PDF, EPUB and Kindle. Combining analysis, geometry, and topology, this volume provides an introduction to current ideas involving the application of $K$-theory of operator algebras to index theory and geometry. In particular, the articles follow two main themes: the use of operator algebras to reflect properties of geometric objects and the application of index theory in settings where the relevant elliptic operators are invertible modulo a $C^*$-algebra other than that of the compact operators. The papers in this collection are the proceedings of the special sessions held at two AMS meetings: the Annual meeting in New Orleans in January 1986, and the Central Section meeting in April 1986. Jonathan Rosenberg's exposition supplies the best available introduction to Kasparov's $KK$-theory and its applications to representation theory and geometry. A striking application of these ideas is found in Thierry Fack's paper, which provides a complete and detailed proof of the Novikov Conjecture for fundamental groups of manifolds of non-positive curvature. Some of the papers involve Connes' foliation algebra and its $K$-theory, while others examine $C^*$-algebras associated to groups and group actions on spaces.
