Outputs (4)

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.