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On the computability of the Steenrod squares

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In questo lavoro offriamo in modo esplicito le formule di una serie de morfismi che controllano la mancanza di commutatività del prodotto cup a livello di cocateni, supponendo di lavorare con insiemi sempliciali; queste formule si stabliliscono in termini di morfismi componenti di una contrazione di Eilenberg-Zilber data. Di conseguenza, nel caso in cui l'insieme sempliciale sia finito in ogni dimensione, otterremo un algoritmo di calcolo di quadrati di Steenrod.


We give explicitely the formulas of a sequence of morphisms which measure the failure of commutativity of the cup product on the cochain level, provided that we work with simplicial sets; these formulas are established in terms of the component morphisms of a given Eilenberg-Zilber contraction. As a consequence, in the case in which the simplicial set is finite in each dimension, we obtain an algorithm for calculating Steenrod squares.

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Correspondence to Pedro Real.

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Real, P. On the computability of the Steenrod squares. Ann. Univ. Ferrara 42, 57–63 (1996).

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Math. Subject Classification (1991)

  • 55S05