TY - JOUR

T1 - Generalizations of a Conway algebra for oriented surface-links via marked graph diagrams

AU - Bae, Yongju

AU - Choi, Seonmi

AU - Kim, Seongjeong

N1 - Publisher Copyright:
© 2018 World Scientific Publishing Company.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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 MÂ 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 MÂ 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.

AB - 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 MÂ 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 MÂ 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.

KW - Conway algebra

KW - conway type invariant

KW - generalized conway algebra

KW - generalized conway type invariant

KW - marked graph

KW - polynomial invariant

KW - surface-link

UR - http://www.scopus.com/inward/record.url?scp=85057579905&partnerID=8YFLogxK

U2 - 10.1142/S0218216518420142

DO - 10.1142/S0218216518420142

M3 - Article

AN - SCOPUS:85057579905

SN - 0218-2165

VL - 27

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 13

M1 - 1842014

ER -