Interactions between Homotopy Theory and Algebra - 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 Interactions between Homotopy Theory and Algebra write by Luchezar L. Avramov. This book was released on 2007. Interactions between Homotopy Theory and Algebra available in PDF, EPUB and Kindle. This book is based on talks presented at the Summer School on Interactions between Homotopy theory and Algebra held at the University of Chicago in the summer of 2004. The goal of this book is to create a resource for background and for current directions of research related to deep connections between homotopy theory and algebra, including algebraic geometry, commutative algebra, and representation theory. The articles in this book are aimed at the audience of beginning researchers with varied mathematical backgrounds and have been written with both the quality of exposition and the accessibility to novices in mind.
Interactions Between Homotopy and Algebra
Interactions Between Homotopy and Algebra - 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 Interactions Between Homotopy and Algebra write by Summer School on Interactions between Homotopy Theory and Algebra. This book was released on 2007. Interactions Between Homotopy and Algebra available in PDF, EPUB and Kindle.
Building Bridges Between Algebra and Topology
Building Bridges Between Algebra and 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 Building Bridges Between Algebra and Topology write by Wojciech Chachólski. This book was released on 2018-03-31. Building Bridges Between Algebra and Topology available in PDF, EPUB and Kindle. This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015. Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.
Homotopy of Operads and Grothendieck-Teichmuller Groups
Homotopy of Operads and Grothendieck-Teichmuller Groups - 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 of Operads and Grothendieck-Teichmuller Groups write by Benoit Fresse. This book was released on 2017-05-22. Homotopy of Operads and Grothendieck-Teichmuller Groups available in PDF, EPUB and Kindle. The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
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.
