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OverviewThe 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* (BR) on B as well as the singular homology H*((BR) 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 N³ 2m 1. Full Product DetailsAuthor: Pascal Lambrechts , Ismar VolicPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 230/1079 Weight: 0.200kg ISBN: 9780821892121ISBN 10: 0821892126 Pages: 116 Publication Date: 30 June 2014 Audience: Professional and scholarly , Professional and scholarly , Professional & Vocational , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsIntroduction 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 BibliographyReviewsAuthor InformationPascal Lambrechts, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium. Ismar Volic, Wellesley College, Massachusetts. Tab Content 6Author Website:Countries AvailableAll regions |
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