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Outputs (6)

Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey (2020)
Book Chapter
Galaz-García, F., Guijarro, L., & Núñez-Zimbrón, J. (2020). Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey. In O. Dearricott, W. Tuschmann, Y. Nikolayevsky, T. Leistner, & D. Crowley (Eds.), Differential geometry in the large (291-310). Cambridge University Press. https://doi.org/10.1017/9781108884136.017

We survey two recent developments in the topic of three-dimensional Alexandrov spaces: the topological classification of closed collapsed threedimensional Alexandrov spaces and the geometrization of sufficiently collapsed closed three-dimensional Ale... Read More about Collapsed 3-Dimensional Alexandrov Spaces: A Brief Survey.

Cohomogeneity one Alexandrov spaces in low dimensions (2020)
Journal Article
Galaz-García, F., & Zarei, M. (2020). Cohomogeneity one Alexandrov spaces in low dimensions. Annals of Global Analysis and Geometry, 58(2), 109-146. https://doi.org/10.1007/s10455-020-09716-7

Alexandrov spaces are complete length spaces with a lower curvature bound in the triangle comparison sense. When they are equipped with an effective isometric action of a compact Lie group with one-dimensional orbit space, they are said to be of coho... Read More about Cohomogeneity one Alexandrov spaces in low dimensions.

Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions (2020)
Journal Article
Corro, D., & Galaz-García, F. (2020). Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions. Proceedings of the American Mathematical Society, 148(7), 3087-3097. https://doi.org/10.1090/proc/14961

We show that for each n 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 u... Read More about Positive Ricci curvature on simply-connected manifolds with cohomogeneity-two torus actions.

Torus actions on rationally elliptic manifolds (2020)
Journal Article
Galaz-García, F., Kerin, M., & Radeschi, M. (2021). Torus actions on rationally elliptic manifolds. Mathematische Zeitschrift, 297, 197-221. https://doi.org/10.1007/s00209-020-02508-6

An upper bound is obtained on the rank of a torus which can act smoothly and effectively on a smooth, closed (simply connected) rationally elliptic manifold. In the maximal-rank case, the manifolds admitting such actions are classified up to equivari... Read More about Torus actions on rationally elliptic manifolds.