The algebra of secondary homotopy operations in ring spectra
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/41904 |
| Acceso en línea: | http://hdl.handle.net/11441/41904 https://doi.org/10.1112/plms/pdq034 |
| Access Level: | acceso abierto |
| Palabra clave: | Ring spectrum homotopy groups secondary homotopy groups Toda bracket Massey product cup-one product Shukla cohomology Mac Lane cohomology permutative category quadratic pair module |
| Sumario: | 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. |
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