Formality of the little Ndisks operad
 Responsibility
 Pascal Lambrechts, Ismar Volić.
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, [2014]
 Copyright notice
 ©2013
 Physical description
 vii, 116 pages : illustrations ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1079.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA3 .A57 NO.1079  Unknown 
More options
Creators/Contributors
 Author/Creator
 Lambrechts, Pascal, 1964 author.
 Contributor
 Volić, Ismar, 1973 author.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Introduction Notation, linear orders, weak partitions, and operads CDGA models for operads Real homotopy theory of semialgebraic sets The FultonMacPherson 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 zigzag of quasiisomorphisms 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 mdisks operad in the little N disks operad when N 2m 1.
(source: Nielsen Book Data)9780821892121 20160613
Subjects
Bibliographic information
 Publication date
 2014
 Copyright date
 2013
 Series
 Memoirs of the American Mathematical Society, 00659266 ; number 1079
 Note
 "Volume 230, number 1079 (first of 5 numbers), July 2014."
 ISBN
 9780821892121 (alk. paper)
 0821892126 (alk. paper)