Geometry & Topology

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

Karsten Grove and Burkhard Wilking

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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

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

Received: 10 December 2013
Revised: 13 June 2014
Accepted: 12 July 2014
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M60: Group actions in low dimensions

nonnegative curvature circle actions knots Alexandrov geometry


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.

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