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A periodicity theorem in homological algebra

1966; Cambridge University Press; Volume: 62; Issue: 3 Linguagem: Inglês

10.1017/s0305004100039955

1469-8064

J. F. Adams,

Advanced Topics in Algebra

Introduction . In (1–3,6) it is shown that homological algebra can be applied to stable homotopy-theory. In this application, we deal with A -modules, where A is the mod p Steenrod algebra. To obtain a concrete geometrical result by this method usually involves work of two distinct sorts. To illustrate this, we consider the spectral sequence of (1,2): Here each group Exts s, t which occurs in the E 2 term can be effectively computed; the process is purely algebraic. However, no such effective method is given for computing the differentials d r in the spectral sequence, or for determining the group extensions by which is built up from the E ∞ term; these are topological problems.