Homology versus homotopy in rational fibrations
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Manuel Amann [1]
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[1] University of Augsburg
University of Augsburg
Kreisfreie Stadt Augsburg, Alemania
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- Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 3, 2022, págs. 857-882
- Idioma: inglés
- DOI: 10.4171/RMI/1298
- Texto completo no disponible (Saber más ...)
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Resumen
Motivated by prominent problems like the Hilali conjecture, Yamaguchi– Yokura recently proposed certain estimates on the relations of the dimensions of rational homotopy and rational cohomology groups of fibre, base and total spaces in a fibration of rationally elliptic spaces.
In this article we prove these estimates in the category of formal elliptic spaces and, in general, whenever the total space in addition has positive Euler characteristic or has the rational homotopy type of a homogeneous manifold (respectively of a known example) of positive sectional curvature. Additionally, we provide general estimates approximating the conjectured ones.
Moreover, we suggest to study families of rationally elliptic spaces under certain asymptotics, and we discuss the conjectured estimates from this perspective for twostage spaces.
