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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 1999 Volume 261, Pages 222–228 (Mi znsl1101)

This article is cited in 3 papers

Order of function on the Bruschlinsky group

S. S. Podkorytov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: For an arbitrary function $F$ defined on the group of homotopy classes of mappings of a finite polyheder $X$ to the circle and taking values in an Abelian group $Q$, the notion of order is defined. The order $\operatorname{ord}F$ is compared with the algebraic degree of $F$. It is proved that $\operatorname{ord} F\le\operatorname{deg}F$ and $\operatorname{deg}F\le\operatorname{dim}X\cdot\operatorname{ord}F$. The inequality $\operatorname{ord}F\ge\operatorname{deg}F$ is proved in the case where $Q$ is torsion-free or $\operatorname{ord}F\le1$.

UDC: 515.143

Received: 31.05.1999


 English version:
Journal of Mathematical Sciences (New York), 2002, 110:4, 2882–2885

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