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On the genus of elliptic fibrations


Author: J.-B. Gatsinzi
Journal: Proc. Amer. Math. Soc. 132 (2004), 597-606
MSC (2000): Primary 55P62; Secondary 55M30
DOI: https://doi.org/10.1090/S0002-9939-03-07203-4
Published electronically: August 20, 2003
MathSciNet review: 2022386
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Abstract: A simply connected topological space is called elliptic if both $\pi_*(X, \mathbb{Q})$ and $H^*(X, \mathbb{Q})$ are finite-dimensional $\mathbb{Q}$-vector spaces. In this paper, we consider fibrations for which the fibre $X$ is elliptic and $ H^*(X, \mathbb{Q}) $ is evenly graded. We show that in the generic cases, the genus of such a fibration is completely determined by generalized Chern classes of the fibration.


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Additional Information

J.-B. Gatsinzi
Affiliation: University of Botswana, Private Bag 0022, Gaborone, Botswana
Email: gatsinzj@mopipi.ub.bw

DOI: https://doi.org/10.1090/S0002-9939-03-07203-4
Keywords: Rational homotopy, Lusternik-Schnirelmann category, genus, sectional category
Received by editor(s): October 6, 2001
Received by editor(s) in revised form: September 19, 2002
Published electronically: August 20, 2003
Additional Notes: Supported by a grant from Université Catholique de Louvain
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society

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