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

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Najib Idrissi

Real Homotopy of Configuration Spaces

Peccot Lecture, Collège de France, March & May 2020

Najib Idrissi

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English

Springer International Publishing AG
12 June 2022

Mathematical foundations; Algebraic topology

Series: Lecture Notes in Mathematics

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.

By: Najib Idrissi
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 2303
Dimensions: Height: 235mm, Width: 155mm,
Weight: 326g
ISBN: 9783031044274
ISBN 10: 3031044274
Series: Lecture Notes in Mathematics
Pages: 187
Publication Date: 12 June 2022
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

- 1. Overview of the Volume. - 2. Configuration Spaces of Manifolds. - 3. Configuration Spaces of Closed Manifolds. - 4. Configuration Spaces of Manifolds with Boundary. - 5. Configuration Spaces and Operads.

Najib Idrissi is a maître de conférences at Université de Paris He completed his PhD at Université de Lille under the supervision of Benoit Fresse and was a postdoctoral researcher at ETH Zürich in the group of Thomas Willwacher. His research interests and experience lie within the theory of operads, a branch of algebraic topology and homological algebra, with a special interest in the study of configuration spaces of manifolds, their links to graph complexes, and the invariants they define. In 2020 he was awarded the Peccot Lecture and Prize by the Collège de France, which rewards “promising mathematicians under 30 who have distinguished themselves in theoretical and applied mathematics.” As part of the award, the author held a series of four lectures in March and May 2020.