Real homotopy of configuration spaces : Peccot Lecture, Collège de France, March & May 2020

Bibliographic Information

Real homotopy of configuration spaces : Peccot Lecture, Collège de France, March & May 2020

Najib Idrissi

(Lecture notes in mathematics, v. 2303)

Springer, 2022

  • : pbk

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Note

Includes bibliographical references (p. 173-182) and index

Description and Table of Contents

Description

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.

Table of Contents

- 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.

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Details

  • NCID
    BC15372448
  • ISBN
    • 9783031044274
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xviii, 185 p.
  • Size
    24 cm
  • Parent Bibliography ID
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