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Introduction

Currently the problem of transferring results of algebraic topology to discrete objects and, in particular, to various categories of digraphs and graphs, is widely investigated. The main technical tools are given by the homotopy theory and various homology theories. We present the basic methods of algebraic topology in graph theory and describe relations between continious and discrete algebraic topology.

Prerequisite

Basic notions of algebra and topology

Reference

1. Grigor'yan A. A., Jimenez Rolando, Muranov Yu. V, Yau Sh.-T. On the path homology theory of digraphs and Eilenberg-Steenrod axioms. Homology, Homotopy and Applications, 2018. Vol. 20. P. 179-205.

2. Grigor'yan A. A., Yong Lin, Muranov Yu. V., Yau Sh.-T. Cohomology of digraphs and (undirected) graphs. Asian Journal of Mathematics, 2015, Vo. 19. No. 5, 887-932.

3. Grigor'yan A. A., Muranov Yu. V., Yau Sh.-T. Graphs associated with simplicial complexes. Homology, Homotopy, and Applications, 2014. Vol.16. 295-311.

4. Grigor'yan A. A., Muranov Yu. V., Yau Sh.-T. On a cohomology of digraphs and Hochschild cohomology. Journal of Homotopy and Related Structures, 2016. Vol. 11, no. 2. P. 209-230.

5. Grigor'yan A. A., Muranov Yu. V. On homology theories of cubical digraphs. Pasfic Journal of Mathematics, 2023. Vol 322. No. 1. //doi.org/10.2140/pjm.2023.322.39