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

Najib Idrissi

ISBN 10: 3031044274 / ISBN 13: 9783031044274

Editore: Springer International Publishing, 2022

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9783031044274

Dati bibliografici

• Titolo: Real Homotopy of Configuration Spaces : Peccot Lecture, Collège de France, March & May 2020
• Editore: Springer International Publishing
• Data di pubblicazione: 2022
• Lingua: Inglese
• ISBN 10: 3031044274
• ISBN 13: 9783031044274
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 12 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 12 millimetri di profondità
• Peso: 324 grammi

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Riassunto

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.

Informazioni sull'autore

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.