The 4-term relation for chord diagrams and framed chord diagrams

During the last seminar talks, Lera Starichkova described the Bollobas-Riordan generalization of the classical Tutte polynomial fromordinary graphs to embedded graphs. The recipe theorem allows one to express the Bollobas-Riordan polynomial of an embedded graphin terms of that for embedded graphs with a single vertex, that is, chord diagrams. Since the Bollobas-Riordan polynomial is definedfor graphs embedded not necessarily into oriented surfaces, framed chord diagrams, as well as ordinary ones are taken into consideration.Slava Zhukov asserts that this function on (framed) chord diagrams satisfies the 4-term relation and is, therefore, a weight system. The goal of the present talk is to recall the seminar where the 4-term relations for both ordinary and framed chord diagrams come form.