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Homotopy of Operads and Grothendieck-Teichmüller Groups : Part 2: The Applications of (Rational) Homotopy Theory Methods

Von:

Fresse, Benoit [aut]

Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: Mathematical Surveys and Monographs ; v. 217Verlag: Providence : American Mathematical Society, 2017Beschreibung: 1 Online-Ressource (743 pages)Schlagwörter:

Andere physische Formen: 9781470434823 | 1470437570. | 9781470437572. | Erscheint auch als: Homotopy of operads and Grothendieck–Teichmüller groups ; Part 2: The applications of (rational) homotopy theory methods. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2017. xxxv, 704 Seiten | Print version: Homotopy of Operads and Grothendieck-Teichmüller Groups : Part 2: The Applications of (Rational) Homotopy Theory Methods. Providence : American Mathematical Society, ©2017DDC-Klassifikation:

514.24

MSC: MSC: *55P48 | 18G55 | 55P10 | 55P62 | 57T05 | 20B27 | 20F36LOC-Klassifikation:

QA612.7.F74 2016

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Zusammenfassung: 5.3. Hom-objects on dg-modules and simplicial modules5.4. Appendix: Contracting chain-homotopies and extra-degeneracies; Chapter 6. Differential Graded Algebras, Simplicial Algebras, and Cosimplicial Algebras; 6.1. The definition of unitary commutative algebras; 6.2. The model category of unitary commutative algebras; 6.3. The bar construction in the category of commutative algebras; Chapter 7. Models for the Rational Homotopy of Spaces; 7.1. The Sullivan cochain dg-algebra associated to a simplicial set; 7.2. The adjunction between dg-algebras and simplicial setsZusammenfassung: Chapter 2. Mapping Spaces and Simplicial Model Categories2.0. The definition of functors on the category of simplicial sets; 2.1. The notion of a simplicial model category; 2.2. Homotopy automorphism spaces; 2.3. Simplicial structures for operads and for algebras over operads; Chapter 3. Simplicial Structures and Mapping Spaces in General Model Categories; 3.1. The Reedy model structures; 3.2. Framing constructions and mapping spaces; 3.3. The definition of geometric realization and totalization functors; 3.4. Appendix: Homotopy ends and coendsZusammenfassung: Chapter 4. Cofibrantly Generated Model Categories4.1. Relative cell complexes and the small object argument; 4.2. The notion of a cofibrantly generated model category; 4.3. Cofibrantly generated model categories and adjunctions; 4.4. Outlook: Combinatorial model categories; Part II(b) . Modules, Algebras, and the Rational Homotopy of Spaces; Chapter 5. Differential Graded Modules, Simplicial Modules, and Cosimplicial Modules; 5.0. Background: dg-modules and simplicial modules; 5.1. The model category of cochain graded dg-modules; 5.2. Monoidal structures and the Eilenberg-Zilber equivalenceZusammenfassung: 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 tPPN: PPN: 1039989608Package identifier: Produktsigel: ZDB-4-NLEBK

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