Path homology theory of multigraphs and quivers

Alexander Grigor’yan; Yuri Muranov; Vladimir Vershinin; Shing-Tung Yau

doi:10.1515/forum-2018-0015

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Path homology theory of multigraphs and quivers

Journal article

Peer reviewed

Path homology theory of multigraphs and quivers

Alexander Grigor’yan, Yuri Muranov, Vladimir Vershinin and Shing-Tung Yau

Forum Mathematicum, Vol.30(5), pp.1319-1337

01/09/2018

DOI: https://doi.org/10.1515/forum-2018-0015

Abstract

Homology of multigraph

homology of quiver

path homology theory

Atkins connectivity graph

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.

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Title: Path homology theory of multigraphs and quivers
Creators - without role: Alexander Grigor’yan - Russian Academy of Sciences
Yuri Muranov
Vladimir Vershinin - Université de Montpellier, Institut Montpelliérain Alexander Grothendieck - IMAG
Shing-Tung Yau - Department of Mathematics [Cambridge]
Publication Details: Forum Mathematicum, Vol.30(5), pp.1319-1337
Identifiers: 9939674109311
Academic Unit: Institut Montpelliérain Alexander Grothendieck - IMAG
Language: English
Resource Type: Journal article
Local Fields: hal-02086358