The Relative Lie Algebra Of Brunnian Braids On Surface

The study of Vassiliev invariants is one of the important topic in knot theory,Vassiliev invariants can be used to distinguish braids and study the properties of braids.The Vassiliev invariant for pure braid groups is induced by the descending central series,and the associated graded Lie algebra induced by the descending central series also called Yang-Baxter Lie algebra,which is very important in mathematical physics.As the normal subgroups of pure braid groups,the Vassiliev invariant for Brunnian braid groups is given by the relative Lie algebra induced by the descending central series of pure braid groups restrict to Brunnian braid groups.In this work,we study the relative Lie algebraL~P(Brun_n(S_g))of Brunnian braid groups on surfaceS_g of genus g with none boundary.We gave a lower bound and an upper bound of this relative Lie algebra.