Rational homotopy of G-manifolds and the geometry of their orbit space

Abstract: A problem by Grove, Wilking, Yeager asks whether a compact, simply connected $G$-manifold with (geometrically) hyperbolic quotient, is (rationally) hyperbolic. We answer this and similar questions in the more general context of variationally complete actions. On the one hand we prove that, under certain conditions (e.g. trivial principal isotropy, or simply connected principal orbits), the $G$-manifold is rationally elliptic if and only if the quotient is flat. On the other hand, without the extra conditions we answer the question in the negative by providing examples of rationally elliptic $G$-manifolds $M$ where $M/G$ admits a hyperbolic metric. This is joint work with Alessandro Minuzzo and Marco Radeschi.

differential geometrymetric geometry

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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