03751nam 2200613 450 991080913320332120170821201330.01-4704-1669-7(CKB)3710000000230216(EBL)3114053(SSID)ssj0001222273(PQKBManifestationID)11707529(PQKBTitleCode)TC0001222273(PQKBWorkID)11195416(PQKB)10635729(MiAaPQ)EBC3114053(RPAM)18076264(PPN)195408640(EXLCZ)99371000000023021620150415h20132013 uy 0engur|n|---|||||txtccrFormality of the little N-disks operad /Pascal Lambrechts, Ismar VolićProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (130 p.)Memoirs of the American Mathematical Society,1947-6221 ;Volume 230, Number 1079"Volume 230, Number 1079 (first of 5 numbers)."0-8218-9212-6 Includes bibliographical references and index.""Contents""; ""Acknowledgments""; ""Chapter 1. Introduction""; ""1. Plan of the paper""; ""Chapter 2. Notation, linear orders, weak partitions, and operads""; ""2.1. Notation""; ""2.2. Linear orders""; ""2.3. Weak ordered partitions""; ""2.4. Operads and cooperads""; ""Chapter 3. CDGA models for operads""; ""Chapter 4. Real homotopy theory of semi-algebraic sets""; ""Chapter 5. The Fulton-MacPherson operad""; ""5.1. Compactification of configuration spaces in â??^{â??}""; ""5.2. The operad structure""; ""5.3. The canonical projections""""5.4. Decomposition of the boundary of [ ] into codimension 0 faces""""5.5. Spaces of singular configurations""; ""5.6. Pullback of a canonical projection along an operad structure map""; ""5.7. Decomposition of the fiberwise boundary along a canonical projection""; ""5.8. Orientation of [ ]""; ""5.9. Proof of the local triviality of the canonical projections""; ""Chapter 6. The CDGAs of admissible diagrams""; ""6.1. Diagrams""; ""6.2. The module ( ) of diagrams""; ""6.3. Product of diagrams""; ""6.4. A differential on the space of diagrams""""6.5. The CDGA ( ) of admissible diagrams""""Chapter 7. Cooperad structure on the spaces of (admissible) diagrams""; ""7.1. Construction of the cooperad structure maps Î?_{ } and Î?_{ }""; ""7.2. Î?_{ } and Î?_{ } are morphisms of algebras""; ""7.3. Î?_{ } is a chain map""; ""7.4. Proof that the cooperad structure is well-defined""; ""Chapter 8. Equivalence of the cooperads and â??*( [â??])""; ""Chapter 9. The Kontsevich configuration space integrals""; ""9.1. Construction of the Kontsevich configuration space integral ""; ""9.2. is a morphism of algebras""""9.3. Vanishing of on non-admissible diagrams""""9.4. and are chain maps""; ""9.5. and are almost morphisms of cooperads""; ""Chapter 10. Proofs of the formality theorems""; ""Index of notation""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 230, Number 1079.Homotopy theoryOperadsLoop spacesHomotopy theory.Operads.Loop spaces.514/.24Lambrechts Pascal1964-1594814Volić Ismar1973-MiAaPQMiAaPQMiAaPQBOOK9910809133203321Formality of the little N-disks operad3915511UNINA