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An orbit space of a nonlinear involution of $ S^2\times S^2$ with nonnegative sectional curvature


Author: Rafael Torres
Journal: Proc. Amer. Math. Soc. 147 (2019), 3523-3532
MSC (2010): Primary 53C20, 53C21, 53B20
DOI: https://doi.org/10.1090/proc/14486
Published electronically: April 8, 2019
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Abstract: We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a homotopy class that was not previously known to contain nonnegatively curved manifolds. The procedure yields new metrics of nonnegative sectional curvature on any 2-sphere bundle with base space the 2-sphere or the real projective plane.


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Additional Information

Rafael Torres
Affiliation: Scuola Internazionale Superiori di Studi Avanzati (SISSA), Via Bonomea 265, 34136, Trieste, Italy
Email: rtorres@sissa.it

DOI: https://doi.org/10.1090/proc/14486
Received by editor(s): April 27, 2017
Received by editor(s) in revised form: November 20, 2018, and November 21, 2018
Published electronically: April 8, 2019
Dedicated: En memoria de Boris Dubrovin
Communicated by: Guofang Wei
Article copyright: © Copyright 2019 American Mathematical Society