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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions
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by Diego Corro and Fernando Galaz-García PDF
Proc. Amer. Math. Soc. 148 (2020), 3087-3097 Request permission

Abstract:

We show that for each $n\geqslant 1$, there exist infinitely many spin and non-spin diffeomorphism types of closed, smooth, simply-connected $(n+4)$-manifolds with a smooth, effective action of a torus $T^{n+2}$ and a metric of positive Ricci curvature invariant under a $T^{n}$-subgroup of $T^{n+2}$. As an application, we show that every closed, smooth, simply-connected $5$- and $6$-manifold admitting a smooth, effective torus action of cohomogeneity two supports metrics with positive Ricci curvature invariant under a circle or $T^2$-action, respectively.
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Additional Information
  • Diego Corro
  • Affiliation: Institut für Algebra und Geometrie, Karlsruher Institut für Technologie (KIT), 76131 Karlsruhe, Germany
  • MR Author ID: 1379059
  • ORCID: 0000-0002-1114-0071
  • Email: diego.corro@partner.kit.edu
  • Fernando Galaz-García
  • Affiliation: Institut für Algebra und Geometrie, Karlsruher Institut für Technologie (KIT), 76131 Karlsruhe, Germany
  • Address at time of publication: Department of Mathematical Sciences, Durham University, Durham, United Kingdom
  • MR Author ID: 822221
  • Email: galazgarcia@kit.edu; fernando.galaz-garcia@durham.ac.uk
  • Received by editor(s): September 19, 2019
  • Received by editor(s) in revised form: December 4, 2019
  • Published electronically: March 31, 2020
  • Additional Notes: The first author was supported by CONACYT-DAAD (scholarship number 409912).
    The second author was supported by the DFG (grant GA 2050 2-1, SPP2026 “Geometry at Infinity”).
    Both authors were supported by the DFG (281869850, RTG 2229 “Asymptotic Invariants and Limits of Groups and Spaces”).
  • Communicated by: Guofang Wei
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 3087-3097
  • MSC (2010): Primary 53C20, 57S15
  • DOI: https://doi.org/10.1090/proc/14961
  • MathSciNet review: 4099795