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

By Jonathan Dinkelbach, B. Leeb. 2008

69 citations recorded by the source corpus.

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, ie there exist invariant locally homogeneous Riemannian metrics. This answers a question posed by Thurston [32]. 57M60, 57M50; 53C21, 53C44

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7c3d01d410263ff764a5131b2de18a1552faeab5

Citations in the corpus

• Geometrisation of 3-Manifolds (2010, unknown): “See also [22].”