Tittel: Homologies on path complexes
Veileder: Abigail Linton
Sammendrag: A path complex generalizes both simplicial complexes and directed graphs. We use the definition of path homology established by Grigor’yan, Lin, Muranov and Yau in [4], which grants a notion of homology on directed graphs. We then construct examples of path complexes that have torsion in their homology group with the goal of studying these homology groups geometrically and demonstrating the notion of torsion in path complexes.