Year: 2022
Type: article
Abstract: For a fixed $N$, we analyze the space of all sequences $z=(z_1,\dots,z_N)$, approximating a continuous function on the circle, with a given persistence diagram $P$, and show that the typical components of this space are homotopy equivalent to $S^1$. We also consider the space of functions on $Y$-shaped (resp., star-shaped) trees with a 2-point persistence diagram, and show that this space is homotopy equivalent to $S^1$ (resp., to a bouquet of circles).
Authors: Konstantin Mischaikow, Charles Weibel
Institution: Rutgers, The State University of New Jersey
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: Topological and Rigorous Computational Methods for High Dimensional Dynamics, Collaborative Research: Revealing the Geometry of Spatio-temporal Chaos with Computational Topology: Theory, Numerics and Experiment, Tripods+X:Res: Collaborative Research: Identification of Gene Regulatory Network Function from Data, HDR TRIPODS: Data Science Principles of the Human-Machine Convergence, Needle in a haystack: effective search for dynamics across the space of networks
OpenAlex ID: W3163552377