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SUMMARY:Ricardo Mendes (The University of Oklahoma)
DTSTART:20260422T150000Z
DTEND:20260422T160000Z
DTSTAMP:20260423T034445Z
UID:VSGS/127
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/127/">R
 ational homotopy of G-manifolds and the geometry of their orbit space</a>\
 nby Ricardo Mendes (The University of Oklahoma) as part of Virtual seminar
  on geometry with symmetries\n\n\nAbstract\nA problem by Grove\, Wilking\,
  Yeager asks whether a compact\, simply connected $G$-manifold with (geome
 trically) hyperbolic quotient\, is (rationally) hyperbolic. We answer this
  and similar questions in the more general context of variationally comple
 te 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. O
 n 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 Alessand
 ro Minuzzo and Marco Radeschi.\n
LOCATION:https://researchseminars.org/talk/VSGS/127/
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