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arXiv · 1802.05871

Non-negatively curved GKM orbifolds

Oliver Goertsches·Michael Wiemeler
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Abstract

In this paper we study non-negatively curved and rationally elliptic GKM$_4$ manifolds and orbifolds. We show that their rational cohomology rings are isomorphic to the rational cohomology of certain model orbifolds. These models are quotients of isometric actions of finite groups on non-negatively curved torus orbifolds. Moreover, we give a simplified proof of a characterisation of products of simplices among orbit spaces of locally standard torus manifolds. This characterisation was originally proved in [Wiemeler, Torus manifolds and non-negative curvature, arXiv:1401.0403] and was used there to obtain a classification of non-negatively curved torus manifolds.

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Oliver Goertsches, Michael Wiemeler. 2021-07-20. Non-negatively curved GKM orbifolds. https://doi.org/10.1007/s00209-021-02853-0

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