A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry
By K. Grove, Burkhard Wilking. 2013
71 citations recorded by the source corpus.
We classify nonnegatively curved simply connected 4-manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is rule out knotted curves in the singular set of the orbit space. As an extension of this work we classify all knots in S^3 which can be realized as an extremal set with respect to an inner metric on S^3 which has nonnegative curvature in the Alexandrov sense.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/e20f3609a23a32ae5c4a4b3656cfa1e80da1e151
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Orientation and Symmetries of Alexandrov Spaces with Applications in Positive Curvature (2012, background): “ion of those strata in X having non-orientable normal cones. Proof. The metric result is all that we need to show. When X is compact and k = 0, the proof is essentially the same as the proof given in [20]. However, in the case where X is non-compact, ork 6= 0 , we need to make slight alterations to ”