
Braiding sequences occur naturally in the study of
the canonical genus of knots. The first talk
gives a description of the canonical Seifert surfaces
of given genus, and a relation to graphs on
surfaces and Bieulerian paths in graphs.
As an application, some estimates on the number of
positive and alternating knots of given genus
are given. In the second talk, diagrams of canonical genus one
and two are discussed in more detail, and a
complete classification is given. If time permits, we will
discuss an algorithm to make any diagram into a special one
without altering the canonical genus. As a consequence,
we have an inequality for the signature of a positive
link related to its Murasugi sum decomposition.
