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

Abstract

We 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].

36 pages. Final version, to appear in Geometry & Topology. Main Theorem extended to actions on hyperbolic 3-manifolds with cusps

References in corpus (3)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Completion of the Proof of the Geometrization Conjecture
• Width and finite extinction time of Ricci flow