Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds

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dc.creatorDinkelbach, Jonathan
dc.creatorLeeb, Bernhard
dc.date2008-01-05
dc.date2009-01-09
dc.date.accessioned2026-07-07T12:27:18Z
dc.date.available2026-07-07T12:27:18Z
dc.descriptionWe apply an equivariant version of Perelman's Ricci flow with surgery to study smooth actions by finite groups on closed 3-manifolds. Our main result is that such actions on elliptic and hyperbolic 3-manifolds are conjugate to isometric actions. Combining our results with results by Meeks and Scott [17], it follows that such actions on geometric 3-manifolds (in the sense of Thurston) are always geometric, i.e. there exist invariant locally homogeneous Riemannian metrics. This answers a question posed by Thurston in [32].
dc.description36 pages. Final version, to appear in Geometry & Topology. Main Theorem extended to actions on hyperbolic 3-manifolds with cusps
dc.identifierhttps://arxiv.org/abs/0801.0803
dc.identifierhttp://arxiv.org/abs/0801.0803
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215164
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject57M60, 57M50 (Primary) 53C21, 53C44 (Secondary)
dc.titleEquivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds
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