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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
Affiliation:
Département de Mathématiques, Université d‘Angers, 2, bd. Lavoisier, 49045 Angers Cedex 01, France; Institute of Mathematics, Romanian Academy, Bucharest, e-mail: [email protected]
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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.

Type
Research Article
Copyright
1998 Kluwer Academic Publishers