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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Volume 30, Issue 5

Issues

Path homology theory of multigraphs and quivers

Alexander Grigor’yan
  • Mathematics Department, University of Bielefeld, Postfach 100131, 33501 Bielefeld, Germany; and Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
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/ Yuri Muranov
  • Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Sloneczna 54 Street, 10-710 Olsztyn, Poland
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/ Vladimir Vershinin
  • Corresponding author
  • Département des Sciences Mathématiques, Université de Montpellier, Place Eugéne Bataillon, 34095 Montpellier cedex 5, France; and Sobolev Institute of Mathematics, Novosibirsk 630090, Russia
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/ Shing-Tung Yau
Published Online: 2018-07-07 | DOI: https://doi.org/10.1515/forum-2018-0015

Abstract

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.

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

MSC 2010: 18G60; 55N35; 55U10; 57M15; 05C25; 05C38

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About the article


Received: 2018-01-16

Revised: 2018-05-28

Published Online: 2018-07-07

Published in Print: 2018-09-01


The first author was partially supported by SFB 1283 of the German Research Council. The second author was partially supported by SFB 1283 of the German Research Council and the CONACyT Grant 284621. The third author was partially supported by CNRS PICS project of cooperation with Georgia, No 237647.


Citation Information: Forum Mathematicum, Volume 30, Issue 5, Pages 1319–1337, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2018-0015.

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