交错链环研究及其推广  

Study of an Alternating Link and Its Generalization

作　　者：万良霞[1] WAN Liangxia(School of Mathematics and Statistics,Beijing Jiaotong University,Beijing,100044,P.R.China)

机构地区：[1]北京交通大学数学与统计学院,北京100044

出　　处：《数学进展》2023年第1期14-24,共11页Advances in Mathematics（China）

摘　　要：纽结理论属于拓扑学的重要分支.由于问题本身的奥妙,因此受到拓扑、代数、几何、组合、图论等领域众多数学家的共同关注.本文介绍交错链环、准交错链环和长路链环的关于Jones多项式及Khovanov同调方面的结果,并给出一些值得进一步研究的问题.Knot theory is an important branch of topology.Because the related problems are very interesting,it receives a lot of attention by mathematicians in the fields of topology,algebra,geometry,combinatorics,graph theory,etc.In this paper we introduce some results of alternating links,quasi-alternating links and long pass links on the Jones polynomial and Khovanov homology.Moreover,some problems are provided worthy of further study.

关 键 词：交错链环 准交错链环 路代换 JONES多项式 Khovanov同调 

分 类 号：O189.24[理学—数学]