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On the path homology of Cayley digraphs and covering digraphs. / Di, S.; Ivanov, S.O.; Mukoseev, L.; Zhang, M.

In: Journal of Algebra, Vol. 653, 01.09.2024, p. 156-199.

Research output: Contribution to journal › Article › peer-review

Harvard

Di, S, Ivanov, SO, Mukoseev, L & Zhang, M 2024, 'On the path homology of Cayley digraphs and covering digraphs', Journal of Algebra, vol. 653, pp. 156-199. https://doi.org/10.1016/j.jalgebra.2024.05.005

APA

Di, S., Ivanov, S. O., Mukoseev, L., & Zhang, M. (2024). On the path homology of Cayley digraphs and covering digraphs. Journal of Algebra, 653, 156-199. https://doi.org/10.1016/j.jalgebra.2024.05.005

Vancouver

Di S, Ivanov SO, Mukoseev L, Zhang M. On the path homology of Cayley digraphs and covering digraphs. Journal of Algebra. 2024 Sep 1;653:156-199. https://doi.org/10.1016/j.jalgebra.2024.05.005

Author

Di, S. ; Ivanov, S.O. ; Mukoseev, L. ; Zhang, M. / On the path homology of Cayley digraphs and covering digraphs. In: Journal of Algebra. 2024 ; Vol. 653. pp. 156-199.

BibTeX

@article{f7fee3a18d754da281a64447250d8771,
title = "On the path homology of Cayley digraphs and covering digraphs",
abstract = "We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a “bridge” between GLMY-theory and group homology theory, which helps to reduce path homology calculations to group homology computations. We show some cases where this approach allows us to fully express path homology in terms of group homology. To illustrate this method, we provide a path homology computation for the Cayley digraph of the additive group of rational numbers with a generating set consisting of inverses to factorials. The main tool in our work is a filtered simplicial set associated with a digraph, which we call the filtered nerve of a digraph. {\textcopyright} 2024 Elsevier Inc.",
keywords = "Cayley graph, Covering, Path homology, Spectral sequence",
author = "S. Di and S.O. Ivanov and L. Mukoseev and M. Zhang",
note = "Цитирования:1 Export Date: 19 October 2024 CODEN: JALGA Адрес для корреспонденции: Ivanov, S.O.; Beijing Institute of Mathematical Sciences and Applications (BIMSA)China; эл. почта: ivanov.s.o.1986@gmail.com Текст о финансировании 1: The work is supported by Beijing Institute of Mathematical Sciences and Applications.",
year = "2024",
month = sep,
day = "1",
doi = "10.1016/j.jalgebra.2024.05.005",
language = "Английский",
volume = "653",
pages = "156--199",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On the path homology of Cayley digraphs and covering digraphs

AU - Di, S.

AU - Ivanov, S.O.

AU - Mukoseev, L.

AU - Zhang, M.

N1 - Цитирования:1 Export Date: 19 October 2024 CODEN: JALGA Адрес для корреспонденции: Ivanov, S.O.; Beijing Institute of Mathematical Sciences and Applications (BIMSA)China; эл. почта: ivanov.s.o.1986@gmail.com Текст о финансировании 1: The work is supported by Beijing Institute of Mathematical Sciences and Applications.

PY - 2024/9/1

Y1 - 2024/9/1

N2 - We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a “bridge” between GLMY-theory and group homology theory, which helps to reduce path homology calculations to group homology computations. We show some cases where this approach allows us to fully express path homology in terms of group homology. To illustrate this method, we provide a path homology computation for the Cayley digraph of the additive group of rational numbers with a generating set consisting of inverses to factorials. The main tool in our work is a filtered simplicial set associated with a digraph, which we call the filtered nerve of a digraph. © 2024 Elsevier Inc.

AB - We develop a theory of covering digraphs, similar to the theory of covering spaces. By applying this theory to Cayley digraphs, we build a “bridge” between GLMY-theory and group homology theory, which helps to reduce path homology calculations to group homology computations. We show some cases where this approach allows us to fully express path homology in terms of group homology. To illustrate this method, we provide a path homology computation for the Cayley digraph of the additive group of rational numbers with a generating set consisting of inverses to factorials. The main tool in our work is a filtered simplicial set associated with a digraph, which we call the filtered nerve of a digraph. © 2024 Elsevier Inc.

KW - Cayley graph

KW - Covering

KW - Path homology

KW - Spectral sequence

UR - https://www.mendeley.com/catalogue/119eb335-f550-3655-b212-560b475f635d/

U2 - 10.1016/j.jalgebra.2024.05.005

DO - 10.1016/j.jalgebra.2024.05.005

M3 - статья

VL - 653

SP - 156

EP - 199

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 126391220