Softcover ISBN:  9782856299913 
Product Code:  SMFMEM/181 
List Price:  $63.00 
AMS Member Price:  $50.40 
Softcover ISBN:  9782856299913 
Product Code:  SMFMEM/181 
List Price:  $63.00 
AMS Member Price:  $50.40 

Book DetailsMémoires de la Société Mathématique de FranceVolume: 181; 2024; 139 ppMSC: Primary 55; 18
A Note to Readers: This book is in French.
Let \(V\) be an elementary abelian 2group and \(X\) be a finite \(V\)\(\mathrm{CW}\)complex.
In this memoir, the authors study two coaugmented cochain complexes of modules over the mod 2 Steenrod algebra \(\mathrm{A}\) equipped with a compatible action of \(\mathrm{H}^{*}V\), the mod 2 cohomology of \(V\), both associated with \(X\). The first, topological complex, is defined using the orbit filtration of \(X\). The second, (algebraic complex), is defined in terms of the unstable \(\mathrm{H}^{*}V\)\(\mathrm{A}\)module structure of \(\mathrm{H}^{*}_{V}X\), the mod 2 equivariant cohomology of \(X\). The authors construct a morphism \(\kappa\) from the algebraic complex into the topological complex.
The authors show, in particular, that both coaugmented complexes are acyclic if, and only if, \(\mathrm{H}^{*}_{V}X\) is free as an \(\mathrm{H}^{*}V\)module. In this case, $\kappa$ is an isomorphism.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

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A Note to Readers: This book is in French.
Let \(V\) be an elementary abelian 2group and \(X\) be a finite \(V\)\(\mathrm{CW}\)complex.
In this memoir, the authors study two coaugmented cochain complexes of modules over the mod 2 Steenrod algebra \(\mathrm{A}\) equipped with a compatible action of \(\mathrm{H}^{*}V\), the mod 2 cohomology of \(V\), both associated with \(X\). The first, topological complex, is defined using the orbit filtration of \(X\). The second, (algebraic complex), is defined in terms of the unstable \(\mathrm{H}^{*}V\)\(\mathrm{A}\)module structure of \(\mathrm{H}^{*}_{V}X\), the mod 2 equivariant cohomology of \(X\). The authors construct a morphism \(\kappa\) from the algebraic complex into the topological complex.
The authors show, in particular, that both coaugmented complexes are acyclic if, and only if, \(\mathrm{H}^{*}_{V}X\) is free as an \(\mathrm{H}^{*}V\)module. In this case, $\kappa$ is an isomorphism.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.