A CHARACTERIZATION OF A PRIMARY OBSTRUCTION OF THE EXISTENCE OF SECTIONS IN FIBER BUNDLES

Rui Marcos de Oliveira BARROS[1]

Carlos BIASI[2]

§    ABSTRACT: The main purpose of this work is to describe the primary obstruction of the existence of sections in a (n-1)- oriented fiber bundle whose fiber is (n-2)-conected. We start generalizing the concept of the Euler class, for (n-1)-oriented fiber bundle and then we prove that this class is the primary obstruction if the fiber is (n-2)-conected.

§    KEYWORDS: Obstructions; fiber bundles; Euler class.

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[1] Departamento de Matemática – FC-UNESP – Campus Bauru – 17033-360 – Bauru – SP.

[2] Departamento de Matemática - Instituto de Ciências Matemáticas de São Carlos - ICMSC - USP - São Carlos - SP.