Divisibility of the Conway polynomial of links

[摘要] The Conway polynomial ∇K = c0 + c1z + c2z2...of a link K is an invariant of links. In this paper we extend a theorem of J. Levine [5] regarding divisibility of the Conway polynomial by monomials of the form zi. Three different definitions of finite type invariants of links are presented, including a definition of surgery finite type. When the coefficients ci are considered as finite type invariants, the type of these invariants is closely related to the degree of the monomials which can be factored out of ∇K. With this in mind, we prove an extension of a conjecture by T. Cochran and P. Melvin [2] concerning the divisibility of an alternating sum sum S

[发布机构] Rice University