Combinatorial Foundation of Homology and Homotopy, Hans-Joachim Baues
Автор: Banyaga Augustin, Hurtubise David Название: Lectures on Morse Homology ISBN: 1402026951 ISBN-13(EAN): 9781402026959 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book presents in great detail all the results one needs to prove the Morse Homology Theorem using classical techniques from algebraic topology and homotopy theory. Most of these results can be found scattered throughout the literature dating from the mid to late 1900's in some form or other, but often the results are proved in different contexts with a multitude of different notations and different goals. This book collects all these results together into a single reference with complete and detailed proofs.The core material in this book includes CW-complexes, Morse theory, hyperbolic dynamical systems (the Lamba-Lemma, the Stable/Unstable Manifold Theorem), transversality theory, the Morse-Smale-Witten boundary operator, and Conley index theory. More advanced topics include Morse theory on Grassmann manifolds and Lie groups, and an overview of Floer homology theories. With the stress on completeness and by its elementary approach to Morse homology, this book is suitable as a textbook for a graduate level course, or as a reference for working mathematicians and physicists.
Автор: H-J. Baues; A. Quintero Название: Infinite Homotopy Theory ISBN: 9401064938 ISBN-13(EAN): 9789401064934 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: In handling non-compact spaces we must take into account the infinity behaviour of such spaces. Later, Freudenthal [ETR] gave a rigorous treatment of the topology of "ideal points" by introducing the space of "ends" of a non-compact space.
Автор: Schwarz Название: Morse Homology ISBN: 3034896883 ISBN-13(EAN): 9783034896887 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 1.1 Background The subject of this book is Morse homology as a combination of relative Morse theory and Conley`s continuation principle. 1.1.1 Classical Morse Theory The fact that Morse theory can be formulated in a homological way is by no means a new idea.
Автор: James W. Vick Название: Homology Theory ISBN: 1461269334 ISBN-13(EAN): 9781461269335 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology. New generations of young mathematicians have been trained, and classical problems have been solved, particularly through the application of geometry and knot theory. Diverse new resources for introductory coursework have appeared, but there is persistent interest in an intuitive treatment of the basic ideas. This second edition has been expanded through the addition of a chapter on covering spaces. By analysis of the lifting problem it introduces the funda- mental group and explores its properties, including Van Kampen's Theorem and the relationship with the first homology group. It has been inserted after the third chapter since it uses some definitions and results included prior to that point. However, much of the material is directly accessible from the same background as Chapter 1, so there would be some flexibility in how these topics are integrated into a course. The Bibliography has been supplemented by the addition of selected books and historical articles that have appeared since 1973.
Автор: Phillip Griffiths; John Morgan Название: Rational Homotopy Theory and Differential Forms ISBN: 1493936999 ISBN-13(EAN): 9781493936991 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham's theorem on simplicial complexes. In addition, Sullivan's results on computing the rational homotopy type from forms is presented.
New to the Second Edition:
*Fully-revised appendices including an expanded discussion of the Hirsch lemma
*Presentation of a natural proof of a Serre spectral sequence result
*Updated content throughout the book, reflecting advances in the area of homotopy theory
With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.
Автор: Kevin P. Knudson Название: Homology of Linear Groups ISBN: 3034895232 ISBN-13(EAN): 9783034895231 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Daniel Quillen`s definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. It presents the stability theorems and low-dimensional results of A. Coverage also examines the Friedlander-Milnor-conjecture concerning the homology of algebraic groups made discrete.
Автор: Jaume Aguade; Carles Broto; Carles Casacuberta Название: Cohomological Methods in Homotopy Theory ISBN: 3034895135 ISBN-13(EAN): 9783034895132 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Peter Gabriel; M. Zisman Название: Calculus of Fractions and Homotopy Theory ISBN: 3642858465 ISBN-13(EAN): 9783642858468 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main purpose of the present work is to present to the reader a particularly nice category for the study of homotopy, namely the homo- topic category (IV). It is also equivalent (I, 1.3) to a category of fractions of the category of topological spaces modulo homotopy, and to the category of Kan complexes modulo homotopy (IV).
Автор: Paul G. Goerss; John F. Jardine Название: Simplicial Homotopy Theory ISBN: 3034897375 ISBN-13(EAN): 9783034897372 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques.
Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature.
Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed.
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