Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2017-05-01

Journal: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals: Scopus、SCIE

Volume: 26

Issue: 6,SI

ISSN: 0218-2165

Key Words: Regional knot invariant; tridle; Alexander polynomial; presentation matrix; linear tridle

Abstract: In this paper, a regional knot invariant is constructed. Like the Wirtinger presentation of a knot group, each planar region contributes a generator, and each crossing contributes a relation. The invariant is called a tridle of the link. As in the quandle theory, one can define Alexander quandle and get Alexander polynomial from it. For link diagram, one can also define a linear tridle and its presentation matrix. A polynomial invariant can be derived from the matrix just like the Alexander polynomial case.