Path homologies of digraphs
Student No.:100
Time:Wed 10:00-11:00, 2017.11.8
Instructor:Alexander Grigoryan  
Place:Lecture hall, Jin Chun Yuan West Bldg.
Starting Date:2017-11-1
Ending Date:2017-11-9

Each digraph (=directed graph) gives rise to a chain complex that is determined by the structure of the paths on the digraph. The homology groups of this chain complex are called path homologies of the digraph. We give examples of complutation of path homologies as well as present some general properties of path homologies:
1. The invariance under homotopy equivalence of digraphs;
2. The Kunneth formulas for Cartesian product and join of digraphs. 

Prerequisite: Linear algebra


[1] Grigor'yan, A., Lin Y., Muranov, Yu., Yau S.-T., Homotopy theory of digraphs, Pure Appl. Math Quaterly 10 (2014) p.619-674
[2] Grigor'yan, A., Muranov, Yu., Yau S.-T., Homologies of digraphs and Künneth formulas, to appear in Comm. Anal. Geom,