Lannes’ T-Functor and the Cohomology of BG
نویسنده
چکیده
Namely, the assumption implies that for every prime p, one has induced isomorphisms H∗>n(BH;Z/p) → H∗>n(BG;Z/p) and thus, by applying the “reconstruction functor”, isomorphisms H∗(BH;Z/p)→ H∗(BG;Z/p). Since BG and BH are spaces of finite type, it follows that the induced map H∗(BH;Z)→ H∗(BG;Z) is an isomorphism too. Thus, by Jackowski [6] and Minami [10], ρ is an isomorphism of Lie groups. In section one we will recall some basic facts concerning the T -functor and in section two we will describe the “reconstruction functor”, following the work of Dwyer and Wilkerson [2]. We will show how this functor can be used to reconstruct certain graded algebras out of their structure in high degrees. In section three we will apply the functor to the cohomology of BG and discuss a few applications.
منابع مشابه
On the torsion in the cohomology of certain mapping spaces
Let p be a prime, and let BV be the classifying space of an elementary abelian p-group V . J. Lannes [L1] has shown that, in many cases, the mod p cohomology of the space of continuous maps Map(BV,X) can be computed by applying an easily defined functor to H∗(X; Z/p). He lets U denote the category of unstable modules over the mod p Steenrod algebra A, and then notes that the functor H∗(BV ) ⊗ :...
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