Generalized group characters and complex oriented cohomology theories

Subrings of singular cohomology associated to spectra

“…The arguments of Green, Hunton and Schuster [4] generalize to prove the following Theorem, using the generalized character theory of Hopkins, Kuhn and Ravenel [7]. There is an analogous result for the Chern subring, which is not stated here explicitly.…”

“…For such theories, there is a description of the cohomology E * (BV) of an elementary abelian p-group in terms of the associated formal group. The work of Hopkins, Kuhn and Ravenel [7] highlights a fundamental property of a cohomology theory, which is termed height-n detection here. This is the key ingredient to the constructions of this paper.…”

“…E (X) to α n H * (X) is an isomorphism in K/N il. For example, the results of Green, Hunton and Schuster [4] concern classifying spaces of finite groups; in this case, Hopkins, Kuhn and Ravenel [7] provide a construction of enough elements in E * -cohomology so as to obtain equality up to F -isomorphism. Proof The hypothesis implies that Q E : [BF n , X] E → [BF n , X] H E is an isomorphism by Proposition 4.1.4.…”

Кольца $K(s)^*(BG)$ для групп $G_{38},…,G_{41}$ порядка 32

“…Конечная группа G называется хорошей [1], если кольцо K-теории Моравы K(s) * (BG) порождено образами классов Эйлера при трансфере. Основным инст-рументом для вычисления аддитивной структуры являются спектральные последо-вательности Атьи-Хирцебруха [2] …”

K(n) Chern approximations of some finite groups

“…Secondly, one has to show that the relations implied by the structure of the representation ring RG suffice. To that end it is enough to produce an upper bound for the rank of the resulting module (which spares us the necessity to use Gröbner basis methods), and compare it to the rank of K.n/ .BG/, which by the first step is given by the Euler characteristic formula of Hopkins, Kuhn and Ravenel [4].…”