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For questions about ring spectra (in homotopy theory).

4 votes
Accepted

If a t-truncation of the unit object in a stable homotopy category is a ring object up to ho...

In the usual stable homotopy category of spectra, the Postnikov truncations of any connective commutative ring are again commutative rings, and the entire Postnikov tower can be enriched to maps of co …
Eric Wofsey's user avatar
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25 votes
Accepted

Are Thom spectra MU, MSO and K-theory spectra KU, KO modules over some truncations of the sp...

For any $k$ and any $0<n<\infty$, $K(n)\wedge \pi_{\leq k}S=0$. Indeed, this is true for any spectrum with finitely many homotopy groups, since $K(n)\wedge H\mathbb{Z}=0$ and any such spectrum has a …
Eric Wofsey's user avatar
  • 31.2k