Overview
- Provides an in-depth discussion of the connection between operads and configuration spaces
- Describes a unified and accessible approach to the use of graph complexes
- Based on 4 lectures held in the framework of the Peccot Lecutre and Prize by the College de France
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2303)
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About this book
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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Table of contents (5 chapters)
Authors and Affiliations
About the author
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.
Bibliographic Information
Book Title: Real Homotopy of Configuration Spaces
Book Subtitle: Peccot Lecture, Collège de France, March & May 2020
Authors: Najib Idrissi
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-031-04428-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
Softcover ISBN: 978-3-031-04427-4Published: 12 June 2022
eBook ISBN: 978-3-031-04428-1Published: 11 June 2022
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XVIII, 187
Number of Illustrations: 32 b/w illustrations, 15 illustrations in colour
Topics: Algebraic Topology, Category Theory, Homological Algebra, Topology