Hits:

Indexed by:期刊论文

Date of Publication:2017-05-01

Journal:JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS

Included Journals:SCIE、Scopus

Volume:26

Issue:6,SI

ISSN No.: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.