## Geometry & Topology

### A knot characterization and $1$–connected nonnegatively curved $4$–manifolds with circle symmetry

#### Abstract

We classify nonnegatively curved simply connected $4$–manifolds with circle symmetry up to equivariant diffeomorphisms. The main problem is to rule out knotted curves in the singular set of the orbit space. As an extension of this work we classify all knots in $S3$ that can be realized as an extremal set with respect to an inner metric on $S3$ that has nonnegative curvature in the Alexandrov sense.

#### Article information

Source
Geom. Topol., Volume 18, Number 5 (2014), 3091-3110.

Dates
Revised: 13 June 2014
Accepted: 12 July 2014
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732889

Digital Object Identifier
doi:10.2140/gt.2014.18.3091

Mathematical Reviews number (MathSciNet)
MR3285230

Zentralblatt MATH identifier
1317.53062

#### Citation

Grove, Karsten; Wilking, Burkhard. A knot characterization and $1$–connected nonnegatively curved $4$–manifolds with circle symmetry. Geom. Topol. 18 (2014), no. 5, 3091--3110. doi:10.2140/gt.2014.18.3091. https://projecteuclid.org/euclid.gt/1513732889

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