Abstract
For an arbitrary function F defined on the group of homotopy classes of mappings of a finite polyhedron X to the circle and taking values in an Abelian group Q, the notion of order is defined. The order ord F is compared with the algebraic degree of F. It is proved that ord F⩽deg F and deg F⩽dim X • ord F. The inequality ord F⩾deg F is proved in the case where Q is torsion-free or ord F⩽1. Bibliography: 2 titles.
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REFERENCES
S. T. Hu, Homotopy Theory, Academic Press, New York (1959).
J. Milnor, Topology from the Differentiable Viewpoint, Univ. Press of Virginia, Charlottesville (1965).
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Podkorytov, S.S. Order of a Function on the Bruschlinsky Group. Journal of Mathematical Sciences 110, 2882–2885 (2002). https://doi.org/10.1023/A:1015322917311
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DOI: https://doi.org/10.1023/A:1015322917311