Lefschetz fixed point theory on fibrations

Author: Manoharan Palanivel  

Publisher: Springer Publishing Company

ISSN: 0025-2611

Source: manuscripta mathematica, Vol.125, Iss.1, 2008-01, pp. : 127-137

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Abstract

For a fibre preserving map Φ: E → E on a fibration (E, , B), we construct a grading preserving map T(Φ, ) between H*(E) and H*(B) that generalizes the Lefschetz number. If T(Φ, ) is an isomorphism between H 0(E) and H 0(B), then  restricts to a surjective local diffeomorphism on each connected component of the fixed point set of Φ under a transversality condition. This yields a characterization for the bundle H → G → G/H to be trivial when 1 (G/H) = 0.