New structures for colored HOMFLY-PT invariants  

作　　者：Shengmao Zhu 

机构地区：[1]Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China [2]Center of Mathematical Sciences,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China Mathematics》2023年第2期341-392,共52页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12061014)。

摘　　要：In this paper,we present several new structures for the colored HOMFLY-PT(Hoste-Ocneanu-Millet-Freyd-Lickorish-Yetter-Przytycki-Traczyk)invariants of framed links.First,we prove the strong integrality property for the normalized colored HOMFLY-PT invariants by purely using the HOMFLY-PT skein theory developed by Morton and his collaborators.By this strong integrality property,we immediately obtain several symmetric properties for the full colored HOMFLY-PT invariants of links.Then we apply our results to refine the mathematical structures appearing in the Labastida-Mari?o-Ooguri-Vafa(LMOV)integrality conjecture for framed links.As another application of the strong integrality,we obtain that the q=1 and a=1 specializations of the normalized colored HOMFLY-PT invariant are well-defined link polynomials.We find that a conjectural formula for the colored Alexander polynomial which is the a=1 specialization of the normalized colored HOMFLY-PT invariant implies that a special case of the LMOV conjecture for framed knots holds.

关 键 词：colored HOMFLY-PT invariant skein theory INTEGRALITY string duality 

分 类 号：O17[理学—数学]