Real Homotopy of Configuration Spaces: Peccot Lecture, Collège de France, March & May 2020

Author(s)
Najib Idrissi.
Publication
Lecture Notes in Mathematics 2303. Cham: Springer, 2022. 210 pp. ISBN: 978-3-031-04427-4.
Online on
Updated on
Accepted on
DOI:10.1007/978-3-031-04428-1
https://doi.org/10.1007/978-3-031-04428-1
hal-03821309
https://hal.science/hal-03821309
MR4461096
https://mathscinet.ams.org/mathscinet/article?mr=4461096
Zbl 07529469
https://zbMath.org/?q=an:07529469

Abstract

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About

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.

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