Homotopy and Singular Homology Groups of Finite Digraphs

Learn about computing algebraic invariants in topological spaces through this mathematics research talk that explores the extension of McCord's theorem to finite digraphs. Discover how to overcome the challenges of infinite dimensionality in chain groups when calculating singular homology and higher homotopy groups, even for finite spaces. Explore the groundbreaking approach of establishing weak homotopy equivalence between finite digraphs and simplicial complexes, enabling practical computations in both pure mathematics and applied fields like data analysis and network science. Gain insights into why traditional methods fall short when working with finite digraphs and how this new theoretical framework provides a solution for calculating higher homotopy groups and singular homology groups through equivalent simplicial complexes.