One of the fundamental problems in the topological
study of polynomial functions
is the computation of the homotopy groups of the
complements of the hypersurface V(f)=f-1(0).
- Zariski and Van Kampen, in the early 1930's,
gave an algorithm for finding a finite presentation
- Libgober (1994) extended the Zariski-Van Kampen
method to give information about
for k � 1 when
V(f) is irreducible.
- Otherwise, much less is known.
We concentrate on the case where f=?i
V(f) is associated to a hyperplane
arrangement.The cohomology of the complement is determined by
combinatorics. As we noticed, this is not true for
the fundamental group and very few is known about
higher homotopy groups. We now focus on the
following problem.Problem: Characterize the arrangements such
that the complement is a K(p,1)-space.Such arrangements are called K(p,1)-
December 1, 2005, 15:00
School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran,