## SECONDARY ALGEBRAS ASSOCIATED TO RING SPECTRA (2006)

by
Hans-joachim Baues
,
Fernando Muro

Citations: | 2 - 1 self |

### BibTeX

@MISC{Baues06secondaryalgebras,

author = {Hans-joachim Baues and Fernando Muro},

title = {SECONDARY ALGEBRAS ASSOCIATED TO RING SPECTRA},

year = {2006}

}

### OpenURL

### Abstract

Abstract. Homotopy groups of a connective ring spectrum R form an-graded algebra π∗R which is commutative if R is commutative. We describe a secondary algebra π∗,∗R which enriches the structure of the algebra π∗R in a new unexpected way. The algebra π∗,∗R encodes secondary homotopy operations in π∗R, such as Toda brackets, and the first Postnikov invariant of R as a ring spectrum. Moreover, π∗,∗R represents a cohomology class in the third Mac Lane cohomology of the algebra π∗R. If R is commutative then π∗,∗R has an E∞-structure and encodes the cup-one squares in π∗R. Contents