The structure of some equivariant Thom spectra

Costenoble, Steven R.

doi:10.1090/S0002-9947-1989-0958887-X

The structure of some equivariant Thom spectra
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by Steven R. Costenoble

Trans. Amer. Math. Soc. 315 (1989), 231-254

DOI: https://doi.org/10.1090/S0002-9947-1989-0958887-X

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Abstract:

We show that the equivariant Thom spectra $M{O_{{{\text {Z}}_2}}}$ and $m{O_{{{\text {Z}}_2}}}$ do not split as wedges of equivariant Eilenberg-Mac Lane spectra, as they do nonequivariantly. This is done by finding two-stage Postnikov towers giving these spectra, and determining the nontrivial $k$-invariants. We also consider the question: In what sense is the spectrum $m{O_{{{\text {Z}}_2}}}$ representing unoriented bordism unique?

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