Zobrazeno 1 - 10
of 18
pro vyhledávání: '"Yuri Muranov"'
Autor:
Yuri Muranov, Anna Szczepkowska
Publikováno v:
Open Mathematics, Vol 19, Iss 1, Pp 706-723 (2021)
In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the con
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8cb6d8884a421e3fc8bbaa407af69bb9
https://doaj.org/article/e7a44c1688f642cbbf7f232ddf74e752
https://doaj.org/article/e7a44c1688f642cbbf7f232ddf74e752
We introduce the weighted path homology on the category of weigh\-ted directed hypergraphs and describe conditions of homotopy invariance of weighted path homology groups. We give several examples that explain the nontriviality of the introduced noti
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c1f770bf226cdb3bb84075ef60770b9a
http://arxiv.org/abs/2204.07813
http://arxiv.org/abs/2204.07813
Publikováno v:
Czechoslovak Mathematical Journal. 68:35-65
We introduce the notion of fundamental groupoid of a digraph and prove its basic properties. In particular, we obtain a product theorem and an analogue of the Van Kampen theorem. Considering the category of (undirected) graphs as the full subcategory
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::638e389e8420424ebe68c4bb7b829cbb
https://doi.org/10.21136/cmj.2018.0683-15
https://doi.org/10.21136/cmj.2018.0683-15
Publikováno v:
Homology, Homotopy and Applications. 20:179-205
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e8cb64b0ba108731e54b870f2651571b
https://doi.org/10.4310/hha.2018.v20.n2.a9
https://doi.org/10.4310/hha.2018.v20.n2.a9
Publikováno v:
Communications in Analysis and Geometry. 25:969-1018
We state and prove Kunneth formulas for path homologies of Cartesian product and join of two digraphs.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e80e82b40b0b348c35df9d8840e5c5f1
https://doi.org/10.4310/cag.2017.v25.n5.a4
https://doi.org/10.4310/cag.2017.v25.n5.a4
Autor:
Anna Szczepkowska, Yuri Muranov
Publikováno v:
Symmetry
Volume 12
Issue 6
Symmetry, Vol 12, Iss 965, p 965 (2020)
Volume 12
Issue 6
Symmetry, Vol 12, Iss 965, p 965 (2020)
In this paper, we construct the colored-path homology theory in the category of vertex colored (di)graphs and describe its basic properties. Our construction is based on the path homology theory of digraphs that was introduced in the papers of Grigor
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d4dc019ba3e70b8bd9e27a51a179c928
https://doi.org/10.3390/sym12060965
https://doi.org/10.3390/sym12060965
Publikováno v:
Forum Mathematicum
Forum Mathematicum, De Gruyter, 2018, 30 (5), pp.1319-1337. ⟨10.1515/forum-2018-0015⟩
Forum Mathematicum, De Gruyter, 2018, 30 (5), pp.1319-1337. ⟨10.1515/forum-2018-0015⟩
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
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::58ca6dea5b665830933df29dd17f981e
https://hal.archives-ouvertes.fr/hal-02086358
https://hal.archives-ouvertes.fr/hal-02086358
Publikováno v:
Journal of Homotopy and Related Structures. 11:209-230
We use a differential form cohomology theory on transitive digraphs to give a new proof of a theorem of Gerstenhaber and Schack about isomorphism between simplicial cohomology and Hochschild cohomology of a certain algebra associated with the simplic
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ff509ae43a8521333978b2ec0d3bf2d4
https://doi.org/10.1007/s40062-015-0103-1
https://doi.org/10.1007/s40062-015-0103-1
Publikováno v:
Asian Journal of Mathematics. 19:887-932
We construct a cohomology theory on a category of finite digraphs (directed graphs), which is based on the universal calculus on the algebra of functions on the vertices of the digraph. We develop necessary algebraic technique and apply it for invest
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::96e06d9df04a83bab794d3e925b6ed60
https://doi.org/10.4310/ajm.2015.v19.n5.a5
https://doi.org/10.4310/ajm.2015.v19.n5.a5
Publikováno v:
Pure and Applied Mathematics Quarterly. 10:619-674
We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy invariance of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fc625c49f832cab223afed3895e5154
https://doi.org/10.4310/pamq.2014.v10.n4.a2
https://doi.org/10.4310/pamq.2014.v10.n4.a2