Homotopy Theory: Tools and Applications, Daniel G. Davis, Hans-Werner Henn, J.F. Jardine, Mark W. Johnson, Charles Rezk

Автор: George W. Whitehead
Название: Elements of Homotopy Theory
ISBN: 0387903364 ISBN-13(EAN): 9780387903361
Издательство: Springer
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Описание: Indeed, if the order in which the results presented here does not strictly correspond to that in which they were discovered, it nevertheless does correspond to an order in which they might have been discovered had those of us who were working in the area been a little more perspicacious.

Автор: John F. Jardine
Название: Local Homotopy Theory
ISBN: 1493940449 ISBN-13(EAN): 9781493940448
Издательство: Springer
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Описание:

Preface.- 1 Introduction.- Part I Preliminaries.- 2 Homotopy theory of simplicial sets.- 3 Some topos theory.- Part II Simplicial presheaves and simplicial sheaves.- 4 Local weak equivalences.- 5 Local model structures.- 6 Cocycles.- 7 Localization theories.- Part III Sheaf cohomology theory.- 8 Homology sheaves and cohomology groups.- 9 Non-abelian cohomology.- Part IV Stable homotopy theory.- 10 Spectra and T-spectra.- 11 Symmetric T-spectra.- References.- Index.

Автор: Vasile Marinca; Nicolae Herisanu
Название: The Optimal Homotopy Asymptotic Method
ISBN: 3319153730 ISBN-13(EAN): 9783319153735
Издательство: Springer
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Описание: The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method.

Автор: Phillip Griffiths; John Morgan
Название: Rational Homotopy Theory and Differential Forms
ISBN: 1493936999 ISBN-13(EAN): 9781493936991
Издательство: Springer
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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.

Автор: Emmanuel D. Farjoun
Название: Cellular Spaces, Null Spaces and Homotopy Localization
ISBN: 3540606041 ISBN-13(EAN): 9783540606048
Издательство: Springer
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Описание: Relates to advances in periodicity in homotopy localization and in cellular spaces. The notion of homotopy localization is treated quite generally and encompasses all the known idempotent homotopy functors. This book is written with an advanced graduate student in topology and research homotopy theorist in mind.

Автор: Riehl
Название: Categorical Homotopy Theory
ISBN: 1107048451 ISBN-13(EAN): 9781107048454
Издательство: Cambridge Academ
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Описание: This categorical perspective on homotopy theory helps consolidate and simplify one`s understanding of derived functors, homotopy limits and colimits, and model categories, among others.

Автор: Bergner, Julia E. (university Of Virginia)
Название: The Homotopy theory of (?,1)-categories
ISBN: 110749902X ISBN-13(EAN): 9781107499027
Издательство: Cambridge Academ
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Описание: Homotopical or ( ,1)-categories have become a significant framework in many areas of mathematics. This book gives an introduction to the different approaches to these structures and the comparisons between them from the perspective of homotopy theory.

Автор: John W. Rutter
Название: Spaces of Homotopy Self-Equivalences - A Survey
ISBN: 3540631038 ISBN-13(EAN): 9783540631033
Издательство: Springer
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Описание: This is a survey of spaces of homotopy self-equivalences. It discusses issues which include: manifolds of three dimensions or more; Whitehead torsion; unions and products; homotopy automorphisms of H-spaces; and nilpotency, rank and group actions.

Автор: Jaume Aguade; Carles Broto; Carles Casacuberta
Название: Cohomological Methods in Homotopy Theory
ISBN: 3034895135 ISBN-13(EAN): 9783034895132
Издательство: Springer
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Автор: Liao Shijun
Название: Advances in the Homotopy Analysis Method
ISBN: 9814551244 ISBN-13(EAN): 9789814551243
Издательство: World Scientific Publishing
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Описание: Unlike other analytic techniques, the Homotopy Analysis Method (HAM) is independent of small/large physical parameters. Besides, it provides great freedom to choose equation type and solution expression of related linear high-order approximation equations. The HAM provides a simple way to guarantee the convergence of solution series. Such uniqueness differentiates the HAM from all other analytic approximation methods. In addition, the HAM can be applied to solve some challenging problems with high nonlinearity.This book, edited by the pioneer and founder of the HAM, describes the current advances of this powerful analytic approximation method for highly nonlinear problems. Coming from different countries and fields of research, the authors of each chapter are top experts in the HAM and its applications.