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ZARISKI–VAN KAMPEN THEOREM FOR HIGHER-HOMOTOPY GROUPS

Published online by Cambridge University Press:  16 September 2003

D. Chéniot  and
A. Libgober
D. Chéniot
Affiliation:
Laboratoire d’Analyse, Topologie et Probabilités (UMR CNRS 6632), Centre de Mathématiques et Informatique, Université de Provence, 39, rue F. Joliot-Curie, 13453 Marseille Cedex 13, France (cheniot@gyptis.univ-mrs.fr)
A. Libgober
Affiliation:
Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607, USA (libgober@math.uic.edu)
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Abstract

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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.

AMS 2000 Mathematics subject classification: Primary 14F35; 14D05; 32S20; 32S50. Secondary 14J70; 32S25; 55P99

Keywords

topology of hypersurface complementshomotopical variation operators
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 2 , Issue 4 , October 2003 , pp. 495 - 527
Copyright
2003 Cambridge University Press