Real Homotopy of Configuration Spaces

Peccot Lecture, Collège de France, March & May 2020

Najib Idrissi (Autor)

Buch | Softcover

XVIII, 187 Seiten

2022 | 1st ed. 2022
Springer International Publishing (Verlag)
978-3-031-04427-4 (ISBN)

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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.

lt;b>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.

- 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.

Erscheinungsdatum	16.06.2022
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XVIII, 187 p. 47 illus., 15 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	324 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Configuration Spaces of Manifolds • Factorization Homology • Fulton-MacPherson Compactifications • Homotopy Invariants of Manifolds • Kontsevich Integrals • operad theory • Poincaré Duality Models • Propagators in Deformation Quantization • rational homotopy theory • Semi-algebraic Forms • Sullivan Models of Spaces
ISBN-10	3-031-04427-4 / 3031044274
ISBN-13	978-3-031-04427-4 / 9783031044274
Zustand	Neuware