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Equivariant Cohomology of Configuration Spaces Mod 2 - The State of the Art (Paperback, 1st ed. 2021)
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Equivariant Cohomology of Configuration Spaces Mod 2 - The State of the Art (Paperback, 1st ed. 2021)
Series: Lecture Notes in Mathematics, 2282
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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.
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