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This article is cited in 1 scientific paper (total in 1 paper)
The order of a homotopy invariant in the stable case
S. S. Podkorytov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
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 $\operatorname{dim} X<2n-1$, 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, stable homotopy, Curtis filtration.
Received: 25.02.2010 and 11.01.2011
Citation:
S. S. Podkorytov, “The order of a homotopy invariant in the stable case”, Mat. Sb., 202:8 (2011), 95–116; Sb. Math., 202:8 (2011), 1183–1206
Linking options:
https://www.mathnet.ru/eng/sm7699https://doi.org/10.1070/SM2011v202n08ABEH004183 https://www.mathnet.ru/eng/sm/v202/i8/p95
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Abstract page: | 354 | Russian version PDF: | 102 | English version PDF: | 4 | References: | 44 | First page: | 19 |
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