Outputs (36)

Free torus actions and twisted suspensions (2024)
Journal Article
Galaz Garcia, F., & Reiser, P. (in press). Free torus actions and twisted suspensions. Forum of Mathematics, Sigma,

We express the total space of a principal circle bundle over a connected sum of two manifolds in terms of the total spaces of circle bundles over each summand, provided certain conditions hold. We then apply this result to provide sufficient conditio... Read More about Free torus actions and twisted suspensions.

Metric geometry of spaces of persistence diagrams (2024)
Journal Article
Che, M., Galaz Garcia, F., Guijarro, L., & Membrillo Solis, I. (2024). Metric geometry of spaces of persistence diagrams. Journal of Applied and Computational Topology, 8(8), 2197-2246. https://doi.org/10.1007/s41468-024-00189-2

Persistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams. In order to do this, we construct a family of... Read More about Metric geometry of spaces of persistence diagrams.

Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods (2024)
Journal Article
Cibotaru, D., & Galaz-García, F. (online). Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods. Annales de l'Institut Fourier, https://doi.org/10.5802/aif.3656

Kurdyka–Łojasiewicz (KŁ) functions are real-valued functions characterized by a differential inequality involving the norm of their gradient. This class of functions is quite rich, containing objects as diverse as subanalytic, transnormal or Morse fu... Read More about Kurdyka–Łojasiewicz functions and mapping cylinder neighborhoods.

Basic metric geometry of the bottleneck distance (2024)
Journal Article
Che, M., Galaz-García, F., Guijarro, L., Membrillo Solis, I., & Valiunas, M. (2024). Basic metric geometry of the bottleneck distance. Proceedings of the American Mathematical Society, 152(8), 3575-3591. https://doi.org/10.1090/proc/16776

Given a metric pair (X, A), i.e. a metric space X and a distinguished closed set A ⊂ X, one may construct in a functorial way a pointed pseudometric space D∞(X, A) of persistence diagrams equipped with the bottleneck distance. We investigate the basi... Read More about Basic metric geometry of the bottleneck distance.

Manifolds that admit a double disk-bundle decomposition (2023)
Journal Article
DeVito, J., Galaz-García, F., & Kerin, M. (2023). Manifolds that admit a double disk-bundle decomposition. Indiana University Mathematics Journal, 72(4), 1503-1551. https://doi.org/10.1512/iumj.2023.72.9408

Three-dimensional Alexandrov spaces: A survey (2022)
Book Chapter
Galaz-García, F., & Núñez-Zimbrón, J. (2022). Three-dimensional Alexandrov spaces: A survey. In G. Arizmendi Echegaray, L. Hernández-Lamoneda, & R. Herrera Guzmán (Eds.), Recent Advances in Alexandrov Geometry (49-88). Springer Verlag. https://doi.org/10.1007/978-3-030-99298-9_2

We survey several results concerning the geometry and topology of threedimensional Alexandrov spaces with the aim of providing a panoramic and up-to-date view of the subject. In particular we present the classification of positively and nonnegatively... Read More about Three-dimensional Alexandrov spaces: A survey.

Cohomogeneity one manifolds and homogeneous spaces of positive scalar curvature (2022)
Journal Article
Frenck, G., Galaz‐García, F., & Reiser, P. (2022). Cohomogeneity one manifolds and homogeneous spaces of positive scalar curvature. Bulletin of the London Mathematical Society, 54(1), 71-82. https://doi.org/10.1112/blms.12557

We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.

Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds (2021)
Journal Article
Eltzner, B., Galaz-García, F., Huckemann, S. F., & Tuschmann, W. (2021). Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds. Proceedings of the American Mathematical Society, 149(9), 3947-3963. https://doi.org/10.1090/proc/15429

We obtain a central limit theorem for closed Riemannian manifolds, clarifying along the way the geometric meaning of some of the hypotheses in Bhattacharya and Lin’s Omnibus central limit theorem for Fréchet means. We obtain our CLT assuming certain... Read More about Stability of the cut locus and a Central Limit Theorem for Fréchet means of Riemannian manifolds.

Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric (2020)
Journal Article
Galaz-García, F., Guijarro, L., & Núñez-Zimbrón, J. (2020). Sufficiently collapsed irreducible Alexandrov 3-spaces are geometric. Indiana University Mathematics Journal, 69(3), 977-1005. https://doi.org/10.1512/iumj.2020.69.7879

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.