Finite orthogonal groups and periodicity of links

الأصل · EN

For a prime number q≠ 2 and r>0 we study, whether there exists an isometry of order qʳ acting on a free Zₚₖ-module equipped with a scalar product. We investigate, whether there exists such an isometry with no non-zero fixed points. Both questions are completely answered in this paper if p≠ 2,q. As an application we refine Naik's criterion for periodicity of links in S³. The periodicity criterion we obtain is effectively computable and gives concrete restrictions for periodicity of low-crossing knots.