Transfer and complex oriented cohomology rings

Abstract

For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces. In turn these results provide universal examples for computing the stable Euler classes (i.e. T r * (1)) and transferred Chern classes for p-fold covers. Applications to the classifying spaces of p-groups are given.

Morava 𝐾-theory rings for the dihedral, semidihedral and generalized quaternion groups in Chern classes

“…The following lemma is an easy consequence of the recursive formula for the FGL given in 4.3.9 of [9]. See [2], Lemma 5.3.…”

“…As for [5,10], there the multiplicative structure is given completely but in terms of artificial generators not equal to Chern classes. Our aim here is to determine the aforementioned multiplicative structure completely in terms of Chern classes by applying the formula for transfer of the first Chern class along double coverings [2], [3].…”

“…We recall the transfer formula from [3] (see also [2]). Let X → X/π be a regular double covering defined by a free involution on X, let ξ → X be a complex line bundle, let ξ π be the transferred bundle and let…”

K(n) Chern approximations of some finite groups

“…Proof Part (i) is stated in Bakuradze and Priddy [2,Lemma 5.3] and (ii) is claimed in Bakuradze and Vershinin [3, Lemma 2.2 (ii)], but, as the referee pointed out, the explanation provided there falls short of a full proof. We therefore give an argument which surely must be the one the authors of [3] had in mind.…”

“…We therefore give an argument which surely must be the one the authors of [3] had in mind. Since we need the notation anyway, we also show (i), the proof being essentially the one from [2].…”