Tbilisi Mathematical Journal

On the cooperation algebra of the connective Adams summand

Andrew Baker and Birgit Richter

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Abstract

The aim of this paper is to gain explicit information about the multiplicative structure of $\ell_*\ell$, where $\ell$ is the connective Adams summand at an odd prime $p$. Our approach differs from Kane's or Lellmann's because our main technical tool is the $MU$-based Künneth spectral sequence. We prove that the algebra structure on $\ell_*\ell$ is inherited from the multiplication on a Koszul resolution of $\ell_*BP$.

Note

We would like to thank Iain Gordon, John Rognes, Steffen Sagave and Sarah White-house for their comments. We also thank the referee for his/her many detailed and helpful remarks. The first author was supported by the Max-Planck Institute for Mathematics, Bonn, and the Yngre Femregande Forskere (YFF) of the Norwegian Research Council; the second author was supported by the Strategisk Universitetsprogram i Ren Matematikk (SUPREMA) of the Norwegian Research Council. We also thank the Universities of Bern, Bonn, and Oslo for their hospitality.

Article information

Source
Tbilisi Math. J., Volume 1 (2008), 33-70.

Dates
Received: 20 March 2007
Revised: 18 March 2008
Accepted: 1 May 2008
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768823

Mathematical Reviews number (MathSciNet)
MR2434436

Zentralblatt MATH identifier
1206.55013

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}
Secondary: 55N20: Generalized (extraordinary) homology and cohomology theories 18G15: Ext and Tor, generalizations, Künneth formula [See also 55U25]

Keywords
connective $K$-theory cooperations Adams summand

Citation

Baker, Andrew; Richter, Birgit. On the cooperation algebra of the connective Adams summand. Tbilisi Math. J. 1 (2008), 33--70. https://projecteuclid.org/euclid.tbilisi/1528768823


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