1,018 research outputs found
Simplified numerical form of universal finite type invariant of Gauss words
In the present paper, we study the finite type invariants of Gauss words. In
the Polyak algebra techniques, we reduce the determination of the group
structure to transformation of a matrix into its Smith normal form and we give
the simplified form of a universal finite type invariant by means of the
isomorphism of this transformation. The advantage of this process is that we
can implement it as a computer program. We obtain the universal finite type
invariant of degree 4, 5, and 6 explicitly. Moreover, as an application, we
give the complete classification of Gauss words of rank 4 and the partial
classification of Gauss words of rank 5 where the distinction of only one pair
remains.Comment: 12 pages, 3 table
- …