Kauffman polynomial of periodic knotted trivalent graphs

摘要

We generalize some of the congruences in [20] to periodicknotted trivalent graphs. As an application, a criterion derived from oneof these congruences is used to obstruct periodicity of links of few crossingsfor the odd primes p = 3, 5, 7, and 11. Moreover, we derive a new criterionof periodic links. In particular, we give a sufficient condition for the periodto divide the crossing number. This gives some progress toward solvingthe well-known conjecture that the period divides the crossing number inthe case of alternating links.