Geodesic
The order of a~homotopy invariant in the stable case
Sbornik. Mathematics, Tome 202 (2011) no. 8, pp. 1183-1206

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Let $X$, $Y$ be cell complexes, let $U$ be an Abelian group, and let $f\colon[X,Y]\to U$ be a homotopy invariant. By definition, the invariant $f$ has order at most $r$ if the characteristic function of the $r$th Cartesian power of the graph of a continuous map $a\colon X\to Y$ determines the value $f([a])$ $\mathbb{Z}$-linearly. It is proved that, in the stable case (that is, when $\operatorname{dim} X2n-1$, and $Y$ is $(n-1)$-connected for some natural number $n$), for a finite cell complex $X$ the order of the invariant $f$ is equal to its degree with respect to the Curtis filtration of the group $[X,Y]$. Bibliography: 9 titles.
Keywords: invariants of finite order
Mots-clés : stable homotopy, Curtis filtration. 
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     author = {S. S. Podkorytov},
     title = {The order of a~homotopy invariant in the stable case},
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S. S. Podkorytov. The order of a~homotopy invariant in the stable case. Sbornik. Mathematics, Tome 202 (2011) no. 8, pp. 1183-1206. http://geodesic.mathdoc.fr/item/SM_2011_202_8_a4/