[from the introduction]: The structure of this work is as follows. In the first chapter, we recall the preliminary notions and results we will make use of, in particular, some facts regarding Coxeter groups and their classifying spaces, results for the homology of 1-loop spaces and Hopf rings. The second chapter is devoted to the exposition of the results involving the cohomology of the symmetric groups. That chapter basically follows the treatment of two published papers, one by Giusti, Salvatore and Sinha, and the other by the author of this thesis. In the third chapter, we calculate the cohomology of the Coxeter groups of Type Bn and Dn as (almost-)Hopf rings. We also carry on the calculation of the restriction to elementary abelian subgroups and of the Steenrod algebra action. Finally, the fourth chapter deals with some results concerning the mod p cohomology of D(X) and Q(X) for a topological space X.

Hopf ring structures on the cohomology of certain spaces / Guerra, Lorenzo; relatore: Salvetti, Mario; Scuola Normale Superiore, 25-Sep-2018.

Hopf ring structures on the cohomology of certain spaces

Guerra, Lorenzo
2018

Abstract

[from the introduction]: The structure of this work is as follows. In the first chapter, we recall the preliminary notions and results we will make use of, in particular, some facts regarding Coxeter groups and their classifying spaces, results for the homology of 1-loop spaces and Hopf rings. The second chapter is devoted to the exposition of the results involving the cohomology of the symmetric groups. That chapter basically follows the treatment of two published papers, one by Giusti, Salvatore and Sinha, and the other by the author of this thesis. In the third chapter, we calculate the cohomology of the Coxeter groups of Type Bn and Dn as (almost-)Hopf rings. We also carry on the calculation of the restriction to elementary abelian subgroups and of the Steenrod algebra action. Finally, the fourth chapter deals with some results concerning the mod p cohomology of D(X) and Q(X) for a topological space X.
25-set-2018
MAT/03 GEOMETRIA
Matematica
algebras
cohomology
Geometry
Hopf ring
Mathematics
Scuola Normale Superiore
Salvetti, Mario
Vistoli, Angelo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/85736
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