[PDF] Hoo Ring Spectra And Their Applications eBook

Author : I.M. James
Publisher : Elsevier
Page : 1336 pages
File Size : 13,44 MB
Release : 1995-07-18
Category : Mathematics
ISBN : 0080532985

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Algebraic topology (also known as homotopy theory) is a flourishing branch of modern mathematics. It is very much an international subject and this is reflected in the background of the 36 leading experts who have contributed to the Handbook. Written for the reader who already has a grounding in the subject, the volume consists of 27 expository surveys covering the most active areas of research. They provide the researcher with an up-to-date overview of this exciting branch of mathematics.

Author : A.T. Fomenko
Publisher : CRC Press
Page : 322 pages
File Size : 24,25 MB
Release : 1998-11-26
Category : Mathematics
ISBN : 9789056990077

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Reflecting the significant contributions of Russian mathematicians to the field, this book contains a selection of papers on tensor and vector analysis. It is divided into three parts, covering Hamiltonian systems, Riemannian geometry and calculus of variations, and topology. The range of applications of these topics is very broad, as many modern geometrical problems recur across a wide range of fields, including mechanics and physics as well as mathematics. Many of the approaches to problems presented in this volume will be novel to the Western reader, although questions are of global interest. The main achievements of the Russian school are placed in the context of the development of each individual subject.

Author : Andrew Baker
Publisher : Cambridge University Press
Page : 246 pages
File Size : 22,22 MB
Release : 2004-11-18
Category : Mathematics
ISBN : 9780521603058

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This book contains some important new contributions to the theory of structured ring spectra.

Author : Andrew J. Blumberg
Publisher : Cambridge University Press
Page : 441 pages
File Size : 47,44 MB
Release : 2022-07-21
Category : Mathematics
ISBN : 1009123297

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A graduate-level introduction to the homotopical technology in use at the forefront of modern algebraic topology.

Author : H.R. Margolis
Publisher : Elsevier
Page : 511 pages
File Size : 14,32 MB
Release : 2011-08-18
Category : Mathematics
ISBN : 0080960170

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I have intended this book to be more than just the sum of its chapters, and the introduction is, in part, an attempt to spell out what the more is. Algebraic topology is the study of topological problems by algebraic means. More precisely, this has come to be framed as the study of topological categories by means of functors to algebraic categories. Beyond the basic definitions and structure, the focus is often on particular problems, for example, Adams’ use of K-theory to solve the vector fields on spheres problem. On the other hand, there are contributions of a more global nature yielding insight into the overall structure of some topological category, for example, Quillen’s work on rational homotopy type. This book is intended primarily as a contribution of this latter sort. So while there will be a variety of particular examples and computations, and although the structure being developed has significant application to many specific problems (some of which are considered here), the major thrust of the text is toward understanding the global structure and linkage of the topological and algebraic categories considered: the stable homotopy category and the category of modules over the Steenrod algebra.

Author : Ulrich Bunke
Publisher : American Mathematical Soc.
Page : 177 pages
File Size : 33,78 MB
Release : 2021-06-21
Category : Education
ISBN : 1470446855

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We develop differential algebraic K-theory for rings of integers in number fields and we construct a cycle map from geometrized bundles of modules over such a ring to the differential algebraic K-theory. We also treat some of the foundational aspects of differential cohomology, including differential function spectra and the differential Becker-Gottlieb transfer. We then state a transfer index conjecture about the equality of the Becker-Gottlieb transfer and the analytic transfer defined by Lott. In support of this conjecture, we derive some non-trivial consequences which are provable by independent means.