Introductory Lectures on Equivariant Cohomology - 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 Introductory Lectures on Equivariant Cohomology write by Loring W. Tu. This book was released on 2020-03-03. Introductory Lectures on Equivariant Cohomology available in PDF, EPUB and Kindle. This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
Introductory Lectures on Equivariant Cohomology
Introductory Lectures on Equivariant Cohomology - 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 Introductory Lectures on Equivariant Cohomology write by Loring W. Tu. This book was released on 2020-03-03. Introductory Lectures on Equivariant Cohomology available in PDF, EPUB and Kindle. This book gives a clear introductory account of equivariant cohomology, a central topic in algebraic topology. Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah-Bott and Berline-Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group action, providing a powerful tool for computing integrals over a manifold. Because integrals and symmetries are ubiquitous, equivariant cohomology has found applications in diverse areas of mathematics and physics. Assuming readers have taken one semester of manifold theory and a year of algebraic topology, Loring Tu begins with the topological construction of equivariant cohomology, then develops the theory for smooth manifolds with the aid of differential forms. To keep the exposition simple, the equivariant localization theorem is proven only for a circle action. An appendix gives a proof of the equivariant de Rham theorem, demonstrating that equivariant cohomology can be computed using equivariant differential forms. Examples and calculations illustrate new concepts. Exercises include hints or solutions, making this book suitable for self-study.
Equivariant Cohomology Theories
Equivariant Cohomology Theories - 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 Equivariant Cohomology Theories write by Glen E. Bredon. This book was released on 2006-11-14. Equivariant Cohomology Theories available in PDF, EPUB and Kindle. a
Equivariant Poincaré Duality on G-Manifolds
Equivariant Poincaré Duality on G-Manifolds - 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 Equivariant Poincaré Duality on G-Manifolds write by Alberto Arabia. This book was released on 2021-06-12. Equivariant Poincaré Duality on G-Manifolds available in PDF, EPUB and Kindle. This book carefully presents a unified treatment of equivariant Poincaré duality in a wide variety of contexts, illuminating an area of mathematics that is often glossed over elsewhere. The approach used here allows the parallel treatment of both equivariant and nonequivariant cases. It also makes it possible to replace the usual field of coefficients for cohomology, the field of real numbers, with any field of arbitrary characteristic, and hence change (equivariant) de Rham cohomology to the usual singular (equivariant) cohomology . The book will be of interest to graduate students and researchers wanting to learn about the equivariant extension of tools familiar from non-equivariant differential geometry.
Lecture Notes on Motivic Cohomology
Lecture Notes on Motivic Cohomology - 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 Lecture Notes on Motivic Cohomology write by Carlo Mazza. This book was released on 2006. Lecture Notes on Motivic Cohomology available in PDF, EPUB and Kindle. The notion of a motive is an elusive one, like its namesake "the motif" of Cezanne's impressionist method of painting. Its existence was first suggested by Grothendieck in 1964 as the underlying structure behind the myriad cohomology theories in Algebraic Geometry. We now know that there is a triangulated theory of motives, discovered by Vladimir Voevodsky, which suffices for the development of a satisfactory Motivic Cohomology theory. However, the existence of motives themselves remains conjectural. This book provides an account of the triangulated theory of motives. Its purpose is to introduce Motivic Cohomology, to develop its main properties, and finally to relate it to other known invariants of algebraic varieties and rings such as Milnor K-theory, etale cohomology, and Chow groups. The book is divided into lectures, grouped in six parts. The first part presents the definition of Motivic Cohomology, based upon the notion of presheaves with transfers. Some elementary comparison theorems are given in this part. The theory of (etale, Nisnevich, and Zariski) sheaves with transfers is developed in parts two, three, and six, respectively. The theoretical core of the book is the fourth part, presenting the triangulated category of motives. Finally, the comparison with higher Chow groups is developed in part five. The lecture notes format is designed for the book to be read by an advanced graduate student or an expert in a related field. The lectures roughly correspond to one-hour lectures given by Voevodsky during the course he gave at the Institute for Advanced Study in Princeton on this subject in 1999-2000. In addition, many of the original proofs have been simplified and improved so that this book will also be a useful tool for research mathematicians. Information for our distributors: Titles in this series are copublished with the Clay Mathematics Institute (Cambridge, MA).
