On the Algebraic Foundations of Bounded 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 On the Algebraic Foundations of Bounded Cohomology write by Theo Bühler. This book was released on 2011. On the Algebraic Foundations of Bounded Cohomology available in PDF, EPUB and Kindle. It is a widespread opinion among experts that (continuous) bounded cohomology cannot be interpreted as a derived functor and that triangulated methods break down. The author proves that this is wrong. He uses the formalism of exact categories and their derived categories in order to construct a classical derived functor on the category of Banach $G$-modules with values in Waelbroeck's abelian category. This gives us an axiomatic characterization of this theory for free, and it is a simple matter to reconstruct the classical semi-normed cohomology spaces out of Waelbroeck's category. The author proves that the derived categories of right bounded and of left bounded complexes of Banach $G$-modules are equivalent to the derived category of two abelian categories (one for each boundedness condition), a consequence of the theory of abstract truncation and hearts of $t$-structures. Moreover, he proves that the derived categories of Banach $G$-modules can be constructed as the homotopy categories of model structures on the categories of chain complexes of Banach $G$-modules, thus proving that the theory fits into yet another standard framework of homological and homotopical algebra.
Bounded Cohomology of Discrete Groups
Bounded Cohomology of Discrete 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 Bounded Cohomology of Discrete Groups write by Roberto Frigerio. This book was released on 2017-11-21. Bounded Cohomology of Discrete Groups available in PDF, EPUB and Kindle. The theory of bounded cohomology, introduced by Gromov in the late 1980s, has had powerful applications in geometric group theory and the geometry and topology of manifolds, and has been the topic of active research continuing to this day. This monograph provides a unified, self-contained introduction to the theory and its applications, making it accessible to a student who has completed a first course in algebraic topology and manifold theory. The book can be used as a source for research projects for master's students, as a thorough introduction to the field for graduate students, and as a valuable landmark text for researchers, providing both the details of the theory of bounded cohomology and links of the theory to other closely related areas. The first part of the book is devoted to settling the fundamental definitions of the theory, and to proving some of the (by now classical) results on low-dimensional bounded cohomology and on bounded cohomology of topological spaces. The second part describes applications of the theory to the study of the simplicial volume of manifolds, to the classification of circle actions, to the analysis of maximal representations of surface groups, and to the study of flat vector bundles with a particular emphasis on the possible use of bounded cohomology in relation with the Chern conjecture. Each chapter ends with a discussion of further reading that puts the presented results in a broader context.
Foundations of Algebraic Topology
Foundations of Algebraic 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 Foundations of Algebraic Topology write by Samuel Eilenberg. This book was released on 2015-12-08. Foundations of Algebraic Topology available in PDF, EPUB and Kindle. The need for an axiomatic treatment of homology and cohomology theory has long been felt by topologists. Professors Eilenberg and Steenrod present here for the first time an axiomatization of the complete transition from topology to algebra. Originally published in 1952. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
A Concise Course in Algebraic Topology
A Concise Course in Algebraic 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 A Concise Course in Algebraic Topology write by J. P. May. This book was released on 1999-09. A Concise Course in Algebraic Topology available in PDF, EPUB and Kindle. Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
