TY - JOUR
AU - Muro, Fernando
AB - In this paper we develop a theory of stable homotopy 2‐groups for spectra which is compatible with the smash product on the structured models for the stable homotopy category, therefore the homotopy 2‐groups of a ring spectrum form a 2‐ring, etc. For instance, 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 triple Toda brackets in π*R. We also describe the secondary model π*, *Q of a commutative ring spectrum Q from which we derive the cup‐one square operation in the graded commutative ring π*Q. As an application we obtain for each ring spectrum R new derivations of the ring π*R.
TI - The algebra of secondary homotopy operations in ring spectra
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/pdq034
DA - 2011-04-01
UR - https://www.deepdyve.com/lp/wiley/the-algebra-of-secondary-homotopy-operations-in-ring-spectra-uQllsaARre
SP - 637
EP - 696
VL - 102
IS - 4
DP - DeepDyve
ER -