## THE ALGEBRA OF SECONDARY HOMOTOPY OPERATIONS IN RING SPECTRA (2007)

by
Hans-joachim Baues
,
Fernando Muro

Citations: | 2 - 1 self |

### BibTeX

@MISC{Baues07thealgebra,

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

title = {THE ALGEBRA OF SECONDARY HOMOTOPY OPERATIONS IN RING SPECTRA},

year = {2007}

}

### OpenURL

### Abstract

Abstract. The primary algebraic model of a ring spectrum R is the ring π∗R of homotopy groups. We introduce the secondary model π∗,∗R which has the structure of a secondary analogue of a ring. The homology of π∗,∗R is π∗R and triple Massey products in π∗,∗R coincide with Toda brackets in π∗R. We also describe the secondary model of a commutative ring spectrum Q from which we derive the cup-one square operation in π∗Q. As an application we obtain for each ring spectrum R new derivations of the ring π∗R. Contents