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Topology at infinity of polynominal mappings and Thom regularity condition

Published online by Cambridge University Press:  04 December 2007

MIHAI TIBĂR
MIHAI TIBĂR
Affiliation:
Département de Mathématiques, Université d‘Angers, 2, bd. Lavoisier, 49045 Angers Cedex 01, France; Institute of Mathematics, Romanian Academy, Bucharest, e-mail: tibar@univ-angers.fr
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Abstract

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We consider polynomial mappings which have atypical fibres due to the asymptotic behavior at infinity. Fixing some proper extension of the polynomial mapping, we study the localizability at infinity of the variation of topology of fibres and the possibility of interpreting local results at infinity into global results. We prove local and global Bertini–Sard–Lefschetz type statements for noncompact spaces and nonproper mappings and we deduce results on the homotopy type or the connectivity of the fibres of polynomial mappings.

Keywords

asymptotic behaviour of polynominal mapssingularities at infinityThom regularity conditionstratified setsLefschetz type resultsrelative conormal
Type
Research Article
Information
Compositio Mathematica , Volume 111 , Issue 1 , March 1998 , pp. 89 - 109
Copyright
1998 Kluwer Academic Publishers