| Abstract: A'Campo
(math.GT/9803081)
has recently given an extremely simple and elegant construction which produces
a fibered link in the 3-sphere from any 1-manifold-with-boundary
generically immersed (with connected image) in the 2-disk (for the
special case of links of complex plane curve singularities, see
math.AG/9710023).
For example, the link corresponding to a generic immersion of the circle
without points of inflection is a closed positive braid. All of A'Campo's
links come equipped with ``complete unfoldings'' (in the sense of Neumann
and Rudolph) into positive quadratic singularities zw=0. I believe (and
hope to have proved by the time of this talk!) that
not only are these unfoldings actually ``Hopf plumbings'', but more
particularly that A'Campo's links are always ``closed T-positive braids''
for an appropriate ``espaliered tree'' T (the tree for ordinary positive
braids is unbranched). |
alexsuciu@neu.edu