Order of function on the Bruschlinsky group

S. S. Podkorytov

Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 4, Tome 261 (1999), pp. 222-228

Résumé

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 $\operatorname{ord}F\le1$.