On Conway's Potential Function for Colored Links  

作　　者：Bo Ju JIANG 

机构地区：[1]Department of Mathematics, Peking University

出　　处：《Acta Mathematica Sinica,English Series》2016年第1期25-39,共15页数学学报（英文版）

基　　金：Partially supported by NSFC(Grant No.#11131008)

摘　　要：The Conway potential function （CPF） for colored links is a convenient version of the multi- variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway＇s ＂smoothing of crossings＂ is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra PnBn, where Bn is a braid group and Pn is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander-Conway polynomial of knots.The Conway potential function （CPF） for colored links is a convenient version of the multi- variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway＇s ＂smoothing of crossings＂ is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra PnBn, where Bn is a braid group and Pn is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander-Conway polynomial of knots.

关 键 词：Colored links Conway potential function Alexander polynomial skein relations 

分 类 号：O174[理学—数学]