39 research outputs found
Basic nets in the projective plane
The notion of basic net (called also basic polyhedron) on plays a
central role in Conway's approach to enumeration of knots and links in .
Drobotukhina applied this approach for links in using basic nets on
. By a result of Nakamoto, all basic nets on can be obtained from a
very explicit family of minimal basic nets (the nets , ,
in Conway's notation) by two local transformations. We prove a similar result
for basic nets in .
We prove also that a graph on is uniquely determined by its pull-back
on (the proof is based on Lefschetz fix point theorem).Comment: 14 pages, 15 figure
C-boundary links up to six crossings
An oriented link is called -boundary if it is realizable as
where is an algebraic curve in
and is an embedded -ball. This notion was introduced by Michel Boileau
and Lee Rudolph in 1995. In a recent joint paper with N.G.Kruzhilin we gave a
complete classification of -boundaries with at most 5 crossings. In
the present paper a more regular method of construction of -boundaries is proposed and the classification is extended up to 6 crossings.Comment: 12 page