Formality of the little N-disks operad
- Pascal Lambrechts, Ismar Volić.
- Providence, Rhode Island : American Mathematical Society, 
- Copyright notice
- Physical description
- vii, 116 pages : illustrations ; 26 cm.
- Memoirs of the American Mathematical Society ; no. 1079.
Math & Statistics Library
|QA3 .A57 NO.1079||Unknown|
- Includes bibliographical references and index.
- Introduction Notation, linear orders, weak partitions, and operads CDGA models for operads Real homotopy theory of semi-algebraic sets The Fulton-MacPherson operad The CDGAs of admissible diagrams Cooperad structure on the spaces of (admissible) diagrams Equivalence of the cooperads D and H * (C[ * ]) The Kontsevich configuration space integrals Proofs of the formality theorems Index of notation Bibliography.
- (source: Nielsen Book Data)9780821892121 20160613
- Publisher's Summary
- The little N -disks operad, B , along with its variants, is an important tool in homotopy theory. It is defined in terms of configurations of disjoint N -dimensional disks inside the standard unit disk in Rn and it was initially conceived for detecting and understanding N -fold loop spaces. Its many uses now stretch across a variety of disciplines including topology, algebra, and mathematical physics. In this paper, the authors develop the details of Kontsevich's proof of the formality of little N -disks operad over the field of real numbers. More precisely, one can consider the singular chains C * ( B R) on B as well as the singular homology H * (( B R) on B . These two objects are operads in the category of chain complexes. The formality then states that there is a zig-zag of quasi-isomorphisms connecting these two operads. The formality also in some sense holds in the category of commutative differential graded algebras. The authors additionally prove a relative version of the formality for the inclusion of the little m-disks operad in the little N -disks operad when N 2m 1.
(source: Nielsen Book Data)9780821892121 20160613
- Publication date
- Copyright date
- Memoirs of the American Mathematical Society, 0065-9266 ; number 1079
- "Volume 230, number 1079 (first of 5 numbers), July 2014."
- 9780821892121 (alk. paper)
- 0821892126 (alk. paper)
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