Frederick R. Cohen – författare

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(ℝ^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(ℝ^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, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and ℓ-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.

This book gives a brief treatment of the equivariant cohomology of the classical configuration space F(ℝ^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(ℝ^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, Blagojević, Lück and Ziegler (2016), who used a claimed intermediate result in order to derive lower bounds for the existence of k-regular and ℓ-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.

The papers in this collection, all fully refereed, originalpapers, reflect many aspects of recent significant advancesin homotopy theory and group cohomology.From the Contents: A. Adem: On the geometry and cohomologyof finite simple groups.- D.J. Benson: Resolutions andPoincar duality for finite groups.- C. Broto and S. Zarati:On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C.Ravenel: Morava K-theories of classifying spaces andgeneralized characters for finite groups.- K. Ishiguro:Classifying spaces of compact simple lie groups and p-tori.-A.T. Lundell: Concise tables of James numbers and somehomotopyof classical Lie groups and associated homogeneousspaces.- J.R. Martino: Anexample of a stable splitting: theclassifying space of the 4-dim unipotent group.- J.E.McClure, L. Smith: On the homotopy uniqueness of BU(2) atthe prime 2.- G. Mislin: Cohomologically central elementsand fusion in groups.

The papers in this collection, all fully refereed, originalpapers, reflect many aspects of recent significant advancesin homotopy theory and group cohomology.From the Contents: A. Adem: On the geometry and cohomologyof finite simple groups.- D.J. Benson: Resolutions andPoincar duality for finite groups.- C. Broto and S. Zarati:On sub-A*-algebras of H*V.- M.J. Hopkins, N.J. Kuhn, D.C.Ravenel: Morava K-theories of classifying spaces andgeneralized characters for finite groups.- K. Ishiguro:Classifying spaces of compact simple lie groups and p-tori.-A.T. Lundell: Concise tables of James numbers and somehomotopyof classical Lie groups and associated homogeneousspaces.- J.R. Martino: Anexample of a stable splitting: theclassifying space of the 4-dim unipotent group.- J.E.McClure, L. Smith: On the homotopy uniqueness of BU(2) atthe prime 2.- G. Mislin: Cohomologically central elementsand fusion in groups.