Handbook of K-Theory

by Eric Friedlander
Handbook of K-Theory
Author: Eric Friedlander
Publisher: Springer Science & Business Media
Total Pages: 1148
Release: 2005-07-18
Genre: Mathematics
ISBN: 354023019X
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This handbook offers a compilation of techniques and results in K-theory. Each chapter is dedicated to a specific topic and is written by a leading expert. Many chapters present historical background; some present previously unpublished results, whereas some present the first expository account of a topic; many discuss future directions as well as open problems. It offers an exposition of our current state of knowledge as well as an implicit blueprint for future research.

The $K$-book

by Charles A. Weibel
The $K$-book
Author: Charles A. Weibel
Publisher: American Mathematical Soc.
Total Pages: 634
Release: 2013-06-13
Genre: Mathematics
ISBN: 0821891324
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Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr

Mixed Motives and Algebraic K-Theory

by Uwe Jannsen
Mixed Motives and Algebraic K-Theory
Author: Uwe Jannsen
Publisher: Springer
Total Pages: 260
Release: 2006-11-14
Genre: Mathematics
ISBN: 3540469419
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The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincaré duality theories, weights, and tensor categories. One thus arrives at generalizations to arbitrary varieties of the Hodge and Tate conjectures to explicit conjectures on l-adic Chern characters for global fields and to certain counterexamples for more general fields. It is to be hoped that these relations ions will in due course be explained by a suitable tensor category of mixed motives. An approximation to this is constructed in the setting of absolute Hodge cycles, by extending this theory to arbitrary varieties. The book can serve both as a guide for the researcher, and as an introduction to these ideas for the non-expert, provided (s)he knows or is willing to learn about K-theory and the standard cohomology theories of algebraic varieties.

K-theory

by Michael Atiyah
K-theory
Author: Michael Atiyah
Publisher: CRC Press
Total Pages: 181
Release: 2018-03-05
Genre: Mathematics
ISBN: 0429973179
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These notes are based on the course of lectures I gave at Harvard in the fall of 1964. They constitute a self-contained account of vector bundles and K-theory assuming only the rudiments of point-set topology and linear algebra. One of the features of the treatment is that no use is made of ordinary homology or cohomology theory. In fact, rational cohomology is defined in terms of K-theory.The theory is taken as far as the solution of the Hopf invariant problem and a start is mode on the J-homomorphism. In addition to the lecture notes proper, two papers of mine published since 1964 have been reproduced at the end. The first, dealing with operations, is a natural supplement to the material in Chapter III. It provides an alternative approach to operations which is less slick but more fundamental than the Grothendieck method of Chapter III, and it relates operations and filtration. Actually, the lectures deal with compact spaces, not cell-complexes, and so the skeleton-filtration does not figure in the notes. The second paper provides a new approach to K-theory and so fills an obvious gap in the lecture notes.

Handbook of Homotopy Theory

by Haynes Miller
Handbook of Homotopy Theory
Author: Haynes Miller
Publisher: CRC Press
Total Pages: 1142
Release: 2020-01-23
Genre: Mathematics
ISBN: 1351251600
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The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Handbook of Measure Theory

by E. Pap
Handbook of Measure Theory
Author: E. Pap
Publisher: Elsevier
Total Pages: 1633
Release: 2002-10-31
Genre: Mathematics
ISBN: 0080533094
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The main goal of this Handbook isto survey measure theory with its many different branches and itsrelations with other areas of mathematics. Mostly aggregating many classical branches of measure theory the aim of the Handbook is also to cover new fields, approaches and applications whichsupport the idea of "measure" in a wider sense, e.g. the ninth part of the Handbook. Although chapters are written of surveys in the variousareas they contain many special topics and challengingproblems valuable for experts and rich sources of inspiration.Mathematicians from other areas as well as physicists, computerscientists, engineers and econometrists will find useful results andpowerful methods for their research. The reader may find in theHandbook many close relations to other mathematical areas: realanalysis, probability theory, statistics, ergodic theory,functional analysis, potential theory, topology, set theory,geometry, differential equations, optimization, variationalanalysis, decision making and others. The Handbook is a richsource of relevant references to articles, books and lecturenotes and it contains for the reader's convenience an extensivesubject and author index.

Handbook of Algebra

by M. Hazewinkel
Handbook of Algebra
Author: M. Hazewinkel
Publisher: Elsevier
Total Pages: 543
Release: 2006-05-30
Genre: Mathematics
ISBN: 0080462499
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Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed.- Thorough and practical source for information- Provides in-depth coverage of new topics in algebra- Includes references to relevant articles, books and lecture notes

Handbook of Number Theory I

by József Sándor
Handbook of Number Theory I
Author: József Sándor
Publisher: Springer Science & Business Media
Total Pages: 638
Release: 2005-11-17
Genre: Mathematics
ISBN: 1402042159
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This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research. Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

Handbook of Self-Regulation, Second Edition

by Kathleen D. Vohs
Handbook of Self-Regulation, Second Edition
Author: Kathleen D. Vohs
Publisher: Guilford Press
Total Pages: 610
Release: 2013-01-18
Genre: Psychology
ISBN: 1462509517
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This authoritative handbook reviews the breadth of current knowledge on the conscious and nonconscious processes by which people regulate their thoughts, emotions, attention, behavior, and impulses. Individual differences in self-regulatory capacities are explored, as are developmental pathways. The volume examines how self-regulation shapes, and is shaped by, social relationships. Failures of self-regulation are also addressed, in chapters on addictions, overeating, compulsive spending, and attention-deficit/hyperactivity disorder. Wherever possible, contributors identify implications of the research for helping people enhance their self-regulatory capacities and pursue desired goals. New to This Edition: * Incorporates significant scientific advances and many new topics. * Increased attention to the social basis of self-regulation. * Chapters on working memory, construal-level theory, temptation, executive functioning in children, self-regulation in older adults, self-harming goal pursuit, interpersonal relationships, religion, and impulsivity as a personality trait.