Computation of Reeb Graphs in a Semi-Algebraic Setting

Explore the computation of Reeb graphs in a semi-algebraic setting through this 31-minute conference talk. Delve into the world of applied topology as the speaker motivates the use of semi-algebraic geometry and demonstrates how Reeb graphs and Reeb spaces of semi-algebraic sets are homeomorphic to semi-algebraic sets. Discover 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. Gain insights into the Reeb graph's ability to track changes in connectivity of level sets of a function and its applications in Morse theory and applied topology.