Cohomology of class groups of cyclotomic fields; an application to Morse- Smale diffeomorphisms (Q1106268)

The author is concerned with describing the 2-part of \(SSF=K_ 0({\mathcal C})/P\) where \(K_ 0({\mathcal C})\) is the Grothendieck group of object pairs (H,u) with H a finitely generated abelian group, and \(u\in Aut(H)\); and where P is the subgroup generated by the classes of permutation modules. SSF is abelian except for its 2-part. Finally the author looks specifically at the Galois cohomology of the 2-part of class groups of abelian number fields and applies these results to the class groups of the fields in the cyclotomic \({\mathbb{Z}}_ 2\)-extension of \({\mathbb{Q}}(\zeta_{16})\).