Zariski-van Kampen theorem for higher homotopy groups

D. Chéniot (1) , A. Libgober

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

This paper gives an extension of the classical Zariski-van Kampen theorem describing the fundamental groups of the complements of plane singular curves by generators and relations. It provides a procedure for computation of the first non-trivial higher homotopy groups of the complements of singular projective hypersurfaces in terms of the homotopy variation operators introduced here.

Domaines: Géométrie algébrique [math.AG]; Topologie algébrique [math.AT]; Variables complexes [math.CV]

D. Chéniot, A. Libgober. Zariski-van Kampen theorem for higher homotopy groups. 2003. ⟨hal-00134786⟩