Geometry & Topology

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

Karsten Grove and Burkhard Wilking

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

Permanent link to this document
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

Subjects
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

Keywords
nonnegative curvature circle actions knots Alexandrov geometry

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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