Stability of Reeb Ordering Method in the Framework of Pospaces

Explore the stability of the Reeb ordering method within the framework of partially ordered spaces (pospaces) in this 46-minute lecture presented by Tomoki Uda for the Applied Algebraic Topology Network. Delve into the significance of Reeb graphs in extracting topological features from contour plots and understand how the Reeb ordering method provides both a natural discretization and an algorithmic approach to compute a Reeb tree. Examine the main theorem establishing the stability of Reeb ordering within the interleaving distance among order-compatible topological spaces. Discover new tools developed in terms of pospaces for manipulating and regarding posets as graph-like objects, including the use of reflection functors for handling nice quotients of pospaces. Gain insights into how the concept of pospaces proves powerful in demonstrating the stability of the Reeb ordering method, enhancing your understanding of applied algebraic topology and its applications in data analysis and visualization.