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Nonnegatively curved $5$–manifolds with almost maximal symmetry rank

Fernando Galaz-Garcia and Catherine Searle

Geometry & Topology 18 (2014) 1397–1435
Abstract

We show that a closed, simply connected, nonnegatively curved 5–manifold admitting an effective, isometric T2 action is diffeomorphic to one of S5,S3 × S2, S3×̃S2 or the Wu manifold SU(3)SO(3).

Keywords
symmetry rank, nonnegative curvature, $5$–manifold, torus action
Mathematical Subject Classification 2010
Primary: 53C20
Secondary: 57S25, 51M25
References
Publication
Received: 5 July 2012
Revised: 8 November 2013
Accepted: 14 December 2013
Published: 7 July 2014
Proposed: John Lott
Seconded: Tobias Colding, Gang Tian
Authors
Fernando Galaz-Garcia
Mathematisches Institut
Westfälische Wilhelms-Universität Münster
Einsteinst. 62
D-48149 Münster
Germany
http://wwwmath.uni-muenster.de/u/fernando.galaz-garcia/
Catherine Searle
Department of Mathematics
Oregon State University
368 Kidder Hall
Corvallis, Oregon 97331
USA
https://sites.google.com/site/catherinesearle1/home