Power operations in the Kunneth spectral sequence and commutative HFp-algebras

Abstract

In this paper, we prove the multiplicativity of the Künneth spectral sequence. This is established by an analogue of the Comparison Theorem from homological algebra, which we suspect may be useful for other spectral sequences. This multiplicativity is then used to compute the action of the Dyer-Lashof algebra on $\HF_p \wedge_{ku} \HF_p$, $\HF_p \wedge_{\BP} \HF_p$, and part of the action on $\HF_p \wedge_{MU} \HF_p$. We then relate these computations to the construction of commutative $R$-algebra structures on commutative $\HF_p$-algebras. In the case of $MU$, we obtain a necessary closure condition on ideals $I\subset M{U}_{\ast }$ such that $MU/I$ can be realized as a commutative $MU$-algebra.

arXiv commentTypos and minor errors fixed. Comments welcome

References in corpus (4)

• On the Adams Spectral Sequence for R-modules
• Multiplicative structures on homotopy spectral sequences II
• Topological André-Quillen homology for cellular commutative $S$-algebras
• Calculating with topological André-Quillen theory, I: Homotopical properties of universal derivations and free commutative $S$-algebras

Cited by in corpus (2)

• Complex cobordism, Hamiltonian loops and global Kuranishi charts
• $E_n$ ring spectra and Dyer-Lashof operations