Homology versus homotopy in fibrations and in limits

  • 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 two-stage spaces.

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Author:Manuel AmannGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/83633
Parent Title (English):arXiv
Year of first Publication:2020
Release Date:2021/02/21
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Differentialgeometrie