Homotopy Theory of C*-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 Homotopy Theory of C*-Algebras write by Paul Arne Østvær. This book was released on 2010-09-08. Homotopy Theory of C*-Algebras available 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.
Rational Homotopy Theory
Rational Homotopy 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 Rational Homotopy Theory write by Yves Felix. This book was released on 2012-12-06. Rational Homotopy Theory available 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.
Homotopy Theory via Algebraic Geometry and Group Representations
Homotopy Theory via Algebraic Geometry and Group Representations - 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 Homotopy Theory via Algebraic Geometry and Group Representations write by Mark E. Mahowald. This book was released on 1998. Homotopy Theory via Algebraic Geometry and Group Representations available 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.
Rings, Modules, and Algebras in Stable Homotopy Theory
Rings, Modules, and Algebras in Stable Homotopy 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 Rings, Modules, and Algebras in Stable Homotopy Theory write by Anthony D. Elmendorf. This book was released on 1997. Rings, Modules, and Algebras in Stable Homotopy Theory available 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
Homotopy Type Theory: Univalent Foundations of Mathematics
Homotopy Type Theory: Univalent Foundations of Mathematics - 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 Homotopy Type Theory: Univalent Foundations of Mathematics write by . This book was released on . Homotopy Type Theory: Univalent Foundations of Mathematics available in PDF, EPUB and Kindle.
