Generalizations of a Conway algebra for oriented surface-links via marked graph diagrams

被引：0

作者：

Bae, Yongju ^{[1
]}

Choi, Seonmi ^{[1
]}

Kim, Seongjeong ^{[2
]}

机构：

[1] Kyungpook Natl Univ, Coll Nat Sci, Dept Math, Daegu, South Korea

[2] Bauman Moscow State Tech Univ, Dept Fundamental Sci, Moscow, Russia

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2018年 / 27卷 / 13期

基金：

新加坡国家研究基金会;

关键词：

Conway algebra; conway type invariant; generalized conway algebra; generalized conway type invariant; marked graph; surface-link; polynomial invariant;

D O I：

10.1142/S0218216518420142

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1987, Przytyski and Traczyk introduced an algebraic structure, called a Conway algebra, and constructed an invariant of oriented links, which is a generalization of the HOMFLY-PT polynomial invariant. In 2018, Kim generalized a Conway algebra, which is an algebraic structure with two skein relations, which is called a generalized Conway algebra. In 2017, Joung, Kamada, Kawauchi and Lee constructed a polynomial invariant of oriented surface-links by using marked graph diagrams. In this paper, we will introduce generalizations MA and (MA) over cap of a Conway algebra and a generalized Conway algebra, which are called a marked Conway algebra and a generalized marked Conway algebra, respectively. We will construct invariants valued in MA and (MA) over cap for oriented marked graphs and oriented surface-links by applying binary operations to classical crossings and marked vertices via marked graph diagrams. The polynomial invariant of oriented surface-links is obtained from the invariant valued in the marked Conway algebra with additional conditions.

引用

页数：26