English

K^*(BG) rings for groups $G=G_{38},...,G_{41}$ of order 32

Algebraic Topology 2016-11-22 v4

Abstract

B. Schuster \cite{SCH1} proved that the modmod 2 Morava KK-theory K(s)(BG)K(s)^*(BG) is evenly generated for all groups GG of order 32. For the four groups GG with the numbers 38, 39, 40 and 41 in the Hall-Senior list \cite{H}, the ring K(2)(BG)K(2)^*(BG) has been shown to be generated as a K(2)K(2)^*-module by transferred Euler classes. In this paper, we show this for arbitrary ss and compute the ring structure of K(s)(BG)K(s)^*(BG). Namely, we show that K(s)(BG)K(s)^*(BG) is the quotient of a polynomial ring in 6 variables over K(s)(pt)K(s)^*(pt) by an ideal for which we list explicit generators.

Keywords

Cite

@article{arxiv.1102.3378,
  title  = {K^*(BG) rings for groups $G=G_{38},...,G_{41}$ of order 32},
  author = {Malkhaz Bakuradze and Mamuka Jibladze},
  journal= {arXiv preprint arXiv:1102.3378},
  year   = {2016}
}

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23 pages