“Bulletin Board”

 School of Mathematics - November 27, 2005

Mathematical Lectures

HOMOTOPY GROUPS of COMPLEMENT of COMPLEX HYPERPLANE ARRANGEMENTS

Michel Jambu
CIMPA and Universite de Nice
Thursday 1 December 2005
15:00
School of Mathematics, IPM

 
 
HOMOTOPY GROUPS of COMPLEMENT of COMPLEX HYPERPLANE ARRANGEMENTS

Michel Jambu
CIMPA and Universite de Nice
Abstract

One of the fundamental problems in the topological study of polynomial functions

f:Cl,0 Cl,0
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 for p1(Cl-V(f)).

- Libgober (1994) extended the Zariski-Van Kampen method to give information about pk(Cl-V(f))?Q for k 1 when V(f) is irreducible.

- Otherwise, much less is known.

We concentrate on the case where f=?i fi and deg(fi)=1, i.e., 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)- arrangements.


Information:

Date:

December 1, 2005, 15:00

Place:

School of Mathematics, Niavaran Bldg., Niavaran Square, Tehran, Iran

 
 
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