We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric properties of maps between compact Riemannian manifolds under curvature restrictions.
Cacciatori, S., Pigola, S. (2017). Hurewicz fibrations, almost submetries and critical points of smooth maps. FORUM MATHEMATICUM, 29(4), 751-760 [10.1515/forum-2016-0009].
Hurewicz fibrations, almost submetries and critical points of smooth maps
PIGOLA, STEFANO
2017
Abstract
We prove that the existence of a Hurewicz fibration between certain spaces with the homotopy type of a CW-complex implies some topological restrictions on their universal coverings. This result is used to deduce differentiable and metric properties of maps between compact Riemannian manifolds under curvature restrictions.
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