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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.

Abstract

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). https://doi.org/10.1007/BF02955020

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Math. Subject Classification (1991)

  • 55S05