Sarah Percival 7/27/22: Computation of Reeb Graphs in a Semi-Algebraic Setting скачать в хорошем качестве

Sarah Percival 7/27/22: Computation of Reeb Graphs in a Semi-Algebraic Setting

The Reeb graph is a tool from Morse theory that has recently found use in applied topology due to its ability to track changes in connectivity of level sets of a function. In this talk, I will motivate the use of semi-algebraic geometry as a setting for problems in applied topology and show that the Reeb graph and, more generally, the Reeb space of a semi-algebraic set is homeomorphic to a semi-algebraic set. This opens up the algorithmic problem of efficiently computing a semi-algebraic description of the Reeb graph. I will then present an algorithm with singly-exponential complexity that realizes the Reeb graph of a function f: X \to R as a semi-algebraic quotient using the roadmap of X with respect to f.