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＜電子ブック＞
Real Homotopy of Configuration Spaces : Peccot Lecture, Collège de France, March & May 2020 / by Najib Idrissi
(Lecture Notes in Mathematics. ISSN:16179692 ; 2303)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
大きさ	XVIII, 187 p. 47 illus., 15 illus. in color : online resource
著者標目	*Idrissi, Najib author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Algebra, Homological LCSH:Manifolds (Mathematics) FREE:Algebraic Topology FREE:Category Theory, Homological Algebra FREE:Manifolds and Cell Complexes
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-031-04428-1

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