Simplicial And Dendroidal Homotopy Theory PDF Download
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| Author | : Gijs Heuts |
| Publisher | : Springer Nature |
| Total Pages | : 622 |
| Release | : 2022-09-03 |
| Genre | : Mathematics |
| ISBN | : 3031104471 |
Download Simplicial and Dendroidal Homotopy Theory Book in PDF, ePub and Kindle
This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.
| Author | : Paul G. Goerss |
| Publisher | : Birkhäuser |
| Total Pages | : 520 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034887078 |
Download Simplicial Homotopy Theory Book in PDF, ePub and Kindle
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.
| Author | : Ieke Moerdijk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 186 |
| Release | : 2010-12-01 |
| Genre | : Mathematics |
| ISBN | : 3034800525 |
Download Simplicial Methods for Operads and Algebraic Geometry Book in PDF, ePub and Kindle
"This book is an introduction to two higher-categorical topics in algebraic topology and algebraic geometry relying on simplicial methods. It is based on lectures delivered at the Centre de Recerca Matemàtica in February 2008, as part of a special year on Homotopy Theory and Higher Categories"--Foreword
| Author | : Paul G. Goerss |
| Publisher | : |
| Total Pages | : 528 |
| Release | : 2010-11-20 |
| Genre | : |
| ISBN | : 9783034601900 |
Download Simplicial Homotopy Theory Book in PDF, ePub and Kindle
| Author | : Paul Gregory Goerss |
| Publisher | : Basel : Birkhäuser Verlag |
| Total Pages | : 510 |
| Release | : 1999-01-01 |
| Genre | : Mathematics |
| ISBN | : 9780817660642 |
Download Simplicial Homotopy Theory Book in PDF, ePub and Kindle
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. This book supplies a modern and detailed exposition of simplicial methods and introduces many of the halle tools of modern holotopy theory. The basic topics as well as more advanced material are discussed, and many results and ideas that are known to experts, but uncollected in the literature, are interspersed throughout the presentation.
| Author | : Eric M. Friedlander |
| Publisher | : Princeton University Press |
| Total Pages | : 196 |
| Release | : 1982-12-21 |
| Genre | : Mathematics |
| ISBN | : 9780691083179 |
Download Etale Homotopy of Simplical Schemes Book in PDF, ePub and Kindle
This book presents a coherent account of the current status of etale homotopy theory, a topological theory introduced into abstract algebraic geometry by M. Artin and B. Mazur. Eric M. Friedlander presents many of his own applications of this theory to algebraic topology, finite Chevalley groups, and algebraic geometry. Of particular interest are the discussions concerning the Adams Conjecture, K-theories of finite fields, and Poincare duality. Because these applications have required repeated modifications of the original formulation of etale homotopy theory, the author provides a new treatment of the foundations which is more general and more precise than previous versions. One purpose of this book is to offer the basic techniques and results of etale homotopy theory to topologists and algebraic geometers who may then apply the theory in their own work. With a view to such future applications, the author has introduced a number of new constructions (function complexes, relative homology and cohomology, generalized cohomology) which have immediately proved applicable to algebraic K-theory.
| Author | : Benoit Fresse |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 743 |
| Release | : 2017-05-22 |
| Genre | : Mathematics |
| ISBN | : 1470434822 |
Download Homotopy of Operads and Grothendieck-Teichmuller Groups Book in PDF, ePub and Kindle
The ultimate goal of this book is to explain that the Grothendieck–Teichmüller group, as defined by Drinfeld in quantum group theory, has a topological interpretation as a group of homotopy automorphisms associated to the little 2-disc operad. To establish this result, the applications of methods of algebraic topology to operads must be developed. This volume is devoted primarily to this subject, with the main objective of developing a rational homotopy theory for operads. The book starts with a comprehensive review of the general theory of model categories and of general methods of homotopy theory. The definition of the Sullivan model for the rational homotopy of spaces is revisited, and the definition of models for the rational homotopy of operads is then explained. The applications of spectral sequence methods to compute homotopy automorphism spaces associated to operads are also explained. This approach is used to get a topological interpretation of the Grothendieck–Teichmüller group in the case of the little 2-disc operad. This volume is intended for graduate students and researchers interested in the applications of homotopy theory methods in operad theory. It is accessible to readers with a minimal background in classical algebraic topology and operad theory.
| Author | : Julia E. Bergner |
| Publisher | : Cambridge University Press |
| Total Pages | : 289 |
| Release | : 2018-03-15 |
| Genre | : Mathematics |
| ISBN | : 1107101360 |
Download The Homotopy Theory of (?,1)-Categories Book in PDF, ePub and Kindle
An introductory treatment to the homotopy theory of homotopical categories, presenting several models and comparisons between them.
| Author | : Paul Selick |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 220 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9780821844366 |
Download Introduction to Homotopy Theory Book in PDF, ePub and Kindle
Offers a summary for students and non-specialists who are interested in learning the basics of algebraic topology. This book covers fibrations and cofibrations, Hurewicz and cellular approximation theorems, topics in classical homotopy theory, simplicial sets, fiber bundles, Hopf algebras, and generalized homology and cohomology operations.
| Author | : John F. Jardine |
| Publisher | : Springer |
| Total Pages | : 508 |
| Release | : 2015-05-27 |
| Genre | : Mathematics |
| ISBN | : 1493923005 |
Download Local Homotopy Theory Book in PDF, ePub and Kindle
This monograph on the homotopy theory of topologized diagrams of spaces and spectra gives an expert account of a subject at the foundation of motivic homotopy theory and the theory of topological modular forms in stable homotopy theory. Beginning with an introduction to the homotopy theory of simplicial sets and topos theory, the book covers core topics such as the unstable homotopy theory of simplicial presheaves and sheaves, localized theories, cocycles, descent theory, non-abelian cohomology, stacks, and local stable homotopy theory. A detailed treatment of the formalism of the subject is interwoven with explanations of the motivation, development, and nuances of ideas and results. The coherence of the abstract theory is elucidated through the use of widely applicable tools, such as Barr's theorem on Boolean localization, model structures on the category of simplicial presheaves on a site, and cocycle categories. A wealth of concrete examples convey the vitality and importance of the subject in topology, number theory, algebraic geometry, and algebraic K-theory. Assuming basic knowledge of algebraic geometry and homotopy theory, Local Homotopy Theory will appeal to researchers and advanced graduate students seeking to understand and advance the applications of homotopy theory in multiple areas of mathematics and the mathematical sciences.
