Formality of the Little N-disks Operad

Pascal Lambrechts, Ismar Volic (Autoren)

Buch | Softcover

116 Seiten

2014
American Mathematical Society (Verlag)
978-0-8218-9212-1 (ISBN)

Titel ist leider vergriffen;
keine Neuauflage

Artikel merken

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* (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.

Pascal Lambrechts, Universite Catholique de Louvain, Louvain-la-Neuve, Belgium. Ismar Volic, Wellesley College, Massachusetts.

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

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	200 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Naturwissenschaften ► Physik / Astronomie
ISBN-10	0-8218-9212-6 / 0821892126
ISBN-13	978-0-8218-9212-1 / 9780821892121
Zustand	Neuware