ON THE PATH HOMOLOGY THEORY OF DIGRAPHS AND EILENBERG-STEENROD AXIOMS

被引：29

作者：

Grigoryan, Alexander ^{[1
,2
]}

Jimenez, Rolando ^{[3
]}

Muranov, Yuri ^{[4
]}

Yau, Shing-Tung ^{[5
]}

机构：

[1] Univ Bielefeld, Math Dept, Postfach 100131, D-33501 Bielefeld, Germany

[2] Russian Acad Sci, Inst Control Sci, Moscow, Russia

[3] UNAM, Inst Matemat, Unidad Oaxaca, Leon 2, Centro 68000, Oaxaca, Mexico

[4] Univ Warmia & Mazury, Fac Math & Comp Sci, Sloneczna 54 St, PL-10710 Olsztyn, Poland

[5] Harvard Univ, Dept Math, One Oxford St, Cambridge, MA 02138 USA

来源：

HOMOLOGY HOMOTOPY AND APPLICATIONS | 2018年 / 20卷 / 02期

关键词：

homology of digraphs; paths in digraphs; homotopy theory for digraphs; Eilenberg-Steenrod axioms; SIMPLICIAL COMPLEXES; DIFFERENTIAL-CALCULUS; CUBIC MANIFOLDS; HOMOTOPY-THEORY; GAUGE-THEORY; GRAPHS; COHOMOLOGY; ALGEBRAS; LATTICES; PATTERNS;

D O I：

10.4310/HHA.2018.v20.n2.a9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper we continue the investigation of the path homology theory of digraphs that was constructed in our previous papers. We prove basic theorems that are similar to the theorems of classical algebraic topology and introduce several natural constructions of digraphs which are very helpful to investigate the path homology theory. We describe relation of our results to the Eilenberg-Steenrod axiomatic of homology theory.

引用

页码：179 / 205

页数：27

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