Equivariant Cohomology of Configuration Spaces Mod 2: The State of the Art by Pavle V. M. Blagojević, Frederick R. Cohen, Michael C. Crabb, Wolfgang Lück, Günter M. Ziegler
English | EPUB | 2022 | 232 Pages | ISBN : 3030841375 | 15.3 MB
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.