S. S. Podkorytov

  1. Order of a homotopy invariant in the stable case.

    Authors: S. S. Podkorytov
    Subjects: Algebraic Topology
    Abstract

    Let X and Y be CW-complexes, U be an abelian group, and f:[X,Y]->U be a map
    (a homotopy invariant). We say that f has order at most r if the characteristic
    function of the r'th Cartesian power of the graph of a continuous map a:X->Y
    Z-linearly determines f([a]). Suppose that the CW-complex X is finite and we
    are in the stable case: dim X<2n-1 and Y is (n-1)-connected. We prove that then
    the order of f equals its degree with respect to the Curtis filtration of the
    group [X,Y].

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