UID:
almahu_9949315532602882
Format:
XVIII, 187 p. 47 illus., 15 illus. in color.
,
online resource.
Edition:
1st ed. 2022.
ISBN:
9783031044281
Series Statement:
Lecture Notes in Mathematics, 2303
Content:
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.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783031044274
Additional Edition:
Printed edition: ISBN 9783031044298
Language:
English
DOI:
10.1007/978-3-031-04428-1
URL:
https://doi.org/10.1007/978-3-031-04428-1
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