Path homology theory of multigraphs and quivers

Alexander Grigor’yan (1) , Yuri Muranov , Vladimir Vershinin (2) , Shing-Tung Yau (3)

1 Universität Bielefeld = Bielefeld University
2 IMAG - Institut Montpelliérain Alexander Grothendieck
3 HARVARD - Department of Mathematics [Cambridge]

We construct a new homology theory for the categories of quivers and multigraphs and describe the basic properties of introduced homology groups. We introduce a conception of homotopy in the category of quivers and we prove the homotopy invariance of homology groups.

Mots clés: Homology of multigraph; homology of quiver; path homology theory; Atkins connectivity graph

Domaines: Mathématiques [math]

Alexander Grigor’yan, Yuri Muranov, Vladimir Vershinin, Shing-Tung Yau. Path homology theory of multigraphs and quivers. Forum Mathematicum, 2018, 30 (5), pp.1319-1337. ⟨10.1515/forum-2018-0015⟩. ⟨hal-02086358⟩