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##

6.1 A comment on Figure 1

It would be worthwhile for the reader to reflect on the relationship
between the relations and the syzygies of and singularities of
plane curves. One such codimension one singularity is the triple point
, which corresponds
to the last two relations above, which can be viewed as ``the motion of a
double point across a line''. One such codimension two singularity is the
quadruple point
,
and it corresponds to the syzygy of Figure 1:
There is a circle-worth of generic deformations of the quadruple
point, corresponding to ``the cross rotating around the target'':
. The different
codimension one singularities along this rotation are exactly the
relations in our syzygy.

Dror Bar-Natan
2001-07-23