Calculating higher digraph homotopy groups
Calculating higher digraph homotopy groups
We give the first tractable and systematic examples of nontrivial higher digraph homotopy groups. To do this we define relative digraph homotopy groups and show these satisfy a long exact sequence analogous to the relative homotopy groups of spaces. We then define digraph suspension and Hurewicz homomorphisms and show they commute with each other. The existence of nontrivial digraph homotopy groups then reduces to the existence of corresponding groups in the degree 1 path homology of digraphs.
digraph, homotopy group, Hurewicz homomorphism, suspension
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Wu, Jie
2ae4aab0-b362-47bd-b494-e25fb2ea0889
Yau, Shing-Tung
cf548ba1-885c-490e-9ad3-f32b5e6ecee4
Zhang, Mengmeng
50e51ac1-7669-4db4-9bc4-47031bf96dc6
Theriault, Stephen
5e442ce4-8941-41b3-95f1-5e7562fdef80
Wu, Jie
2ae4aab0-b362-47bd-b494-e25fb2ea0889
Yau, Shing-Tung
cf548ba1-885c-490e-9ad3-f32b5e6ecee4
Zhang, Mengmeng
50e51ac1-7669-4db4-9bc4-47031bf96dc6
Theriault, Stephen, Wu, Jie, Yau, Shing-Tung and Zhang, Mengmeng
(2026)
Calculating higher digraph homotopy groups.
Science China Mathematics.
(doi:10.1007/s11425-025-2575-8).
Abstract
We give the first tractable and systematic examples of nontrivial higher digraph homotopy groups. To do this we define relative digraph homotopy groups and show these satisfy a long exact sequence analogous to the relative homotopy groups of spaces. We then define digraph suspension and Hurewicz homomorphisms and show they commute with each other. The existence of nontrivial digraph homotopy groups then reduces to the existence of corresponding groups in the degree 1 path homology of digraphs.
Text
digraph homotopy groups final
- Accepted Manuscript
Restricted to Repository staff only until 17 March 2027.
Available under License Other.
Request a copy
More information
Accepted/In Press date: 9 March 2026
e-pub ahead of print date: 17 March 2026
Keywords:
digraph, homotopy group, Hurewicz homomorphism, suspension
Identifiers
Local EPrints ID: 511113
URI: http://eprints.soton.ac.uk/id/eprint/511113
ISSN: 1869-1862
PURE UUID: 862cfc3e-ba87-4be2-b200-46c8ab182c14
Catalogue record
Date deposited: 05 May 2026 16:32
Last modified: 06 May 2026 01:45
Export record
Altmetrics
Contributors
Author:
Jie Wu
Author:
Shing-Tung Yau
Author:
Mengmeng Zhang
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
