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Mat. Sb., 2011, Volume 202, Number 8, Pages 95–116 (Mi msb7699)  

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.

DOI: https://doi.org/10.4213/sm7699

Full text: PDF file (674 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2011, 202:8, 1183–1206

Bibliographic databases:

Document Type: Article
UDC: 515.142.424
MSC: 55Q05, 55P42
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

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. S. Podkorytov, “On homotopy invariants of finite degree”, J. Math. Sci. (N. Y.), 212:5 (2016), 587–604  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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