Erratum to “Transferred Chern classes in Morava 𝐾-theory”

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

“…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…”

Morava K(s)*-rings of the extensions of Cp by the products of good groups under diagonal action

“…In a previous article [5] the author and S. Priddy obtained formulas relating Chern classes of transfer bundles to transfers of Chern classes. As formal consequences of such formulas one obtains new relations (as well as often much simpler derivations of old ones), and the hope generally is that these combined methods prove sufficient.…”

MoravaK-theory rings for the groupsG38, …,G41of order 32

“…K.s/ .BG/ be the associated transfer homomorphism induced by the stable transfer map [1], [15], [10]. We will need the following transfer formula from [7].…”

“…It is proved in [19] that K.s/ .BG/ is evenly generated and for s D 2 is generated by Euler classes and transferred Euler classes. One consequence of our main theorem below is that this is true for any s. We obtain generators for the ideal R above by using the formula for transferred Euler class from [7] and follow a certain plan, which proved to be sufficient to handle the 2-groups D, SD, QD, Q [9], [6] and modular p-groups [4]. For a discussion of the ring structure of all other groups of order 32 see [19], [20].…”