Equivariant $E$-Theory for $C^*$-Algebras PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Equivariant $E$-Theory for $C^*$-Algebras PDF full book. Access full book title Equivariant $E$-Theory for $C^*$-Algebras by Erik Guentner. Download full books in PDF and EPUB format.
Author: Erik Guentner
Publisher: American Mathematical Soc.
ISBN: 0821821164
Category : Mathematics
Languages : en
Pages : 101
Get Book
Book Description
This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space
Author: Erik Guentner
Publisher: American Mathematical Soc.
ISBN: 0821821164
Category : Mathematics
Languages : en
Pages : 101
Get Book
Book Description
This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space
Author: Michael A. Hill
Publisher: Cambridge University Press
ISBN: 1108831443
Category : Mathematics
Languages : en
Pages : 881
Get Book
Book Description
A complete and definitive account of the authors' resolution of the Kervaire invariant problem in stable homotopy theory.
Author: Alain Connes
Publisher: Springer Science & Business Media
ISBN: 9783540203575
Category : Mathematics
Languages : en
Pages : 372
Get Book
Book Description
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.
Author: Bogdan Bojarski
Publisher: Springer Science & Business Media
ISBN: 3764376872
Category : Mathematics
Languages : en
Pages : 327
Get Book
Book Description
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.
Author: Laura Ann Smithies
Publisher: American Mathematical Soc.
ISBN: 0821827251
Category : Mathematics
Languages : en
Pages : 106
Get Book
Book Description
This book is intended for graduate students and research mathematicians interested in topological groups, Lie groups, category theory, and homological algebra.
Author: Liming Ge
Publisher: American Mathematical Soc.
ISBN: 0821810936
Category : Mathematics
Languages : en
Pages : 416
Get Book
Book Description
This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered were $C*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.
Author: J. Peter May
Publisher: American Mathematical Soc.
ISBN: 0821803190
Category : Mathematics
Languages : en
Pages : 384
Get Book
Book Description
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
Author: L. Gaunce Jr. Lewis
Publisher: Springer
ISBN: 3540470778
Category : Mathematics
Languages : en
Pages : 548
Get Book
Book Description
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.
Author: Eric Friedlander
Publisher: Springer Science & Business Media
ISBN: 354023019X
Category : Mathematics
Languages : en
Pages : 1148
Get Book
Book Description
This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.
Author: Robert S. Doran
Publisher: American Mathematical Soc.
ISBN: 1470419483
Category : Operator algebras
Languages : en
Pages : 267
Get Book
Book Description
his volume contains the proceedings of the AMS Special Session Operator Algebras and Their Applications: A Tribute to Richard V. Kadison, held from January 10ā11, 2015, in San Antonio, Texas. Richard V. Kadison has been a towering figure in the study of operator algebras for more than 65 years. His research and leadership in the field have been fundamental in the development of the subject, and his influence continues to be felt though his work and the work of his many students, collaborators, and mentees. Among the topics addressed in this volume are the Kadison-Kaplanksy conjecture, classification of Cā-algebras, connections between operator spaces and parabolic induction, spectral flow, Cā-algebra actions, von Neumann algebras, and applications to mathematical physics.
