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We classify nonnegatively curved simply connected 4-manifolds with circlesymmetry up to equivariant diffeomorphisms. The main problem is rule outknotted curves in the singular set of the orbit space. As an extension of thiswork we classify all knots in S^3 which can be realized as an extremal set withrespect to an inner metric on S^3 which has nonnegative curvature in theAlexandrov sense.

A knot characterization and 1-connected nonnegatively curved 4-manifolds with circle symmetry