Homotopy Theory Of C Algebras PDF Download
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Author | : Paul Arne Østvær |
Publisher | : Springer Science & Business Media |
Total Pages | : 142 |
Release | : 2010-09-08 |
Genre | : Mathematics |
ISBN | : 303460565X |
Download Homotopy Theory of C*-Algebras Book in PDF, ePub and Kindle
Homotopy theory and C* algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications.
Author | : Yves Felix |
Publisher | : Springer Science & Business Media |
Total Pages | : 574 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 146130105X |
Download Rational Homotopy Theory Book in PDF, ePub and Kindle
Rational homotopy theory is a subfield of algebraic topology. Written by three authorities in the field, this book contains all the main theorems of the field with complete proofs. As both notation and techniques of rational homotopy theory have been considerably simplified, the book presents modern elementary proofs for many results that were proven ten or fifteen years ago.
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Download Homotopy Type Theory: Univalent Foundations of Mathematics Book in PDF, ePub and Kindle
Author | : Anthony D. Elmendorf |
Publisher | : American Mathematical Soc. |
Total Pages | : 265 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 0821843036 |
Download Rings, Modules, and Algebras in Stable Homotopy Theory Book in PDF, ePub and Kindle
This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ``$S$-modules'' whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ``$S$-algebras'' and ``commutative $S$-algebras'' in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a
Author | : Paul Selick |
Publisher | : American Mathematical Soc. |
Total Pages | : 220 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9780821844366 |
Download Introduction to Homotopy Theory Book in PDF, ePub and Kindle
Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
Author | : Mark E. Mahowald |
Publisher | : American Mathematical Soc. |
Total Pages | : 394 |
Release | : 1998 |
Genre | : Mathematics |
ISBN | : 0821808052 |
Download Homotopy Theory via Algebraic Geometry and Group Representations Book in PDF, ePub and Kindle
The academic year 1996-97 was designated as a special year in Algebraic Topology at Northwestern University (Evanston, IL). In addition to guest lecturers and special courses, an international conference was held entitled "Current trends in algebraic topology with applications to algebraic geometry and physics". The series of plenary lectures included in this volume indicate the great breadth of the conference and the lively interaction that took place among various areas of mathematics. Original research papers were submitted, and all submissions were refereed to the usual journal standards.
Author | : |
Publisher | : Academic Press |
Total Pages | : 383 |
Release | : 1975-11-12 |
Genre | : Mathematics |
ISBN | : 0080873804 |
Download Homotopy Theory: An Introduction to Algebraic Topology Book in PDF, ePub and Kindle
Homotopy Theory: An Introduction to Algebraic Topology
Author | : Douglas C. Ravenel |
Publisher | : Princeton University Press |
Total Pages | : 228 |
Release | : 1992-11-08 |
Genre | : Mathematics |
ISBN | : 9780691025728 |
Download Nilpotence and Periodicity in Stable Homotopy Theory Book in PDF, ePub and Kindle
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Author | : M. Rørdam |
Publisher | : Cambridge University Press |
Total Pages | : 260 |
Release | : 2000-07-20 |
Genre | : Mathematics |
ISBN | : 9780521789448 |
Download An Introduction to K-Theory for C*-Algebras Book in PDF, ePub and Kindle
This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.
Author | : Gerald J. Murphy |
Publisher | : Academic Press |
Total Pages | : 297 |
Release | : 2014-06-28 |
Genre | : Mathematics |
ISBN | : 0080924964 |
Download C*-Algebras and Operator Theory Book in PDF, ePub and Kindle
This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.