Formality of the Little N-disks Operad.
Lambrechts, Pascal.
Formality of the Little N-disks Operad. - 1st ed. - 1 online resource (130 pages) - Memoirs of the American Mathematical Society ; v.230 . - Memoirs of the American Mathematical Society .
Intro -- 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 ℝ^ -- 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 Ψ_ and Ψ_ -- 7.2. Ψ_ and Ψ_ are morphisms of algebras -- 7.3. Ψ_ is a chain map -- 7.4. Proof that the cooperad structure is well-defined -- Chapter 8. Equivalence of the cooperads and ℋ*( [∙]) -- 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.
9781470416690
Homotopy theory.
Operads.
Loop spaces.
Electronic books.
QA612.7 -- .L36 2013eb
514/.24
Formality of the Little N-disks Operad. - 1st ed. - 1 online resource (130 pages) - Memoirs of the American Mathematical Society ; v.230 . - Memoirs of the American Mathematical Society .
Intro -- 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 ℝ^ -- 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 Ψ_ and Ψ_ -- 7.2. Ψ_ and Ψ_ are morphisms of algebras -- 7.3. Ψ_ is a chain map -- 7.4. Proof that the cooperad structure is well-defined -- Chapter 8. Equivalence of the cooperads and ℋ*( [∙]) -- 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.
9781470416690
Homotopy theory.
Operads.
Loop spaces.
Electronic books.
QA612.7 -- .L36 2013eb
514/.24