Real Homotopy of Configuration Spaces

Released on by Najib Idrissi
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  • Real Homotopy of Configuration Spaces Book Detail

  • Author : Najib Idrissi
  • Release Date : 2022-06-11
  • Publisher : Springer Nature
  • Genre : Mathematics
  • Pages : 201
  • ISBN 13 : 3031044282
  • File Size : 3,3 MB
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Real Homotopy of Configuration Spaces by Najib Idrissi PDF Summary

Book 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.

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Real Homotopy of Configuration Spaces

Real Homotopy of Configuration Spaces

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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. Configuratio

Cohomological Methods in Homotopy Theory

Cohomological Methods in Homotopy Theory

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This book contains a collection of articles summarizing the state of knowledge in a large portion of modern homotopy theory. A call for articles was made on the