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28 votes
2 answers
2k views

Has anyone seen a nice map of multiplicative cohomology theories?

I have seen lots of descriptions of this map in the literature but never seen it nicely drawn anywhere. I could try to do it myself but I really lack expertise, hence am afraid to miss something or ...
მამუკა ჯიბლაძე's user avatar
19 votes
1 answer
1k views

What are explicit obstructions to realizability of formal group laws as complex-oriented ring spectra?

Recall that a complex-oriented spectrum is a ring spectrum E with a map $MU \to E$. Analogously, a ring with a (1-d commutative) formal group law is (represented by) a ring $R$ with a map $L \to R$ (...
Catherine Ray's user avatar
16 votes
1 answer
608 views

Multiplicative Brown representability?

The Brown representability theorem can be convenient way to construct a spectrum. But to get a ring spectrum of even a very unstructured form seems to be harder. There's even currently a statement on ...
Tim Campion's user avatar
12 votes
1 answer
703 views

Does the spectrum of Morava E-theory depend only on height?

I almost expect the answer to this question to be no, but I can't find it explicitly said anywhere. Given a formal group law $f$ of height $n$ over a perfect field $k$ of characteristic $p$, we can ...
Sofía Marlasca Aparicio's user avatar
4 votes
0 answers
176 views

Have mod $p^k$ Dyer Lashof operations been studied?

Here is one of the motivations for my question, when $p=2$. The homology of the spectrum $H\mathbb F_2$ as an algebra is generated by the Dyer Lashof operations on the single generator $\xi_1$ (and it ...
elidiot's user avatar
  • 283
3 votes
1 answer
157 views

Concrete pull-back calculation along H-space map

I am trying to calculate the pull-back of a cohomology class on the loopspace of the algebraic $K$-theory space $\Omega K(\mathbb{C})$ along the H-space map of $K(\mathbb{C}).$ Let $b_k\in \tilde{H}^{...
Christopher Ohrt's user avatar