Bibliographic Information

Equivariant cohomology of configuration spaces mod 2 : the state of the art

Pavle V. M. Blagojević ... [et al.]

(Lecture notes in mathematics, 2282)

Springer, c2021

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Other authors: Frederick R. Cohen, Michael C. Crabb, Wolfgang Lück, Günter M. Ziegler

Includes bibliographical references (p. 201-205) and index

Description and Table of Contents

Description

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F( ^d,n) from its beginnings to recent developments. This subject has been studied intensively, starting with the classical papers of Artin (1925/1947) on the theory of braids, and progressing through the work of Fox and Neuwirth (1962), Fadell and Neuwirth (1962), and Arnol'd (1969). The focus of this book is on the mod 2 equivariant cohomology algebras of F( ^d,n), whose additive structure was described by Cohen (1976) and whose algebra structure was studied in an influential paper by Hung (1990). A detailed new proof of Hung's main theorem is given, however it is shown that some of the arguments given by him on the way to his result are incorrect, as are some of the intermediate results in his paper.This invalidates a paper by three of the authors, Blagojevic, Luck and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and -skew embeddings. Using the new proof of Hung's main theorem, new lower bounds for the existence of highly regular embeddings are obtained: Some of them agree with the previously claimed bounds, some are weaker. Assuming only a standard graduate background in algebraic topology, this book carefully guides the reader on the way into the subject. It is aimed at graduate students and researchers interested in the development of algebraic topology in its applications in geometry.

Table of Contents

- 1. Snapshots from the History. - Part I Mod 2 Cohomology of Configuration Spaces. - 2. The Ptolemaic Epicycles Embedding. - 3. The Equivariant Cohomology of Pe(Rd, 2m). - 4. Hu'ng's Injectivity Theorem. - Part II Applications to the (Non-)Existence of Regular and Skew Embeddings. - 5. On Highly Regular Embeddings: Revised. - 6. More Bounds for Highly Regular Embeddings. - Part III Technical Tools. - 7. Operads. - 8. The Dickson Algebra. - 9. The Stiefel-Whitney Classes of the Wreath Square of a Vector Bundle. - 10. Miscellaneous Calculations.

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Details
  • NCID
    BC11704375
  • ISBN
    • 9783030841379
  • Country Code
    sz
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Cham
  • Pages/Volumes
    xix, 208 p.
  • Size
    24 cm
  • Parent Bibliography ID
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