Real Homotopy of Configuration Spaces - Peccot Lecture, College de France, March & May 2020 (Paperback, 1st ed. 2022)

This volume provides a unified and accessible account of recent developments regarding the real homotopy type of configuration spaces of manifolds. Configuration spaces consist of collections of pairwise distinct points in a given manifold, the study of which is a classical topic in algebraic topology. One of this theory's most important questions concerns homotopy invariance: if a manifold can be continuously deformed into another one, then can the configuration spaces of the first manifold be continuously deformed into the configuration spaces of the second? This conjecture remains open for simply connected closed manifolds. Here, it is proved in characteristic zero (i.e. restricted to algebrotopological invariants with real coefficients), using ideas from the theory of operads. A generalization to manifolds with boundary is then considered. Based on the work of Campos, Ducoulombier, Lambrechts, Willwacher, and the author, the book covers a vast array of topics, including rational homotopy theory, compactifications, PA forms, propagators, Kontsevich integrals, and graph complexes, and will be of interest to a wide audience.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2303
Release date:	June 2022
First published:	2022
Authors:	Najib Idrissi
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	187
Edition:	1st ed. 2022
ISBN-13:	978-3-03-104427-4
Categories:	Books > Science & Mathematics > Mathematics > Mathematical foundations > General Books > Science & Mathematics > Mathematics > Topology > Algebraic topology
LSN:	3-03-104427-4
Barcode:	9783031044274

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