Local indicability in the presence of diagrammatic reducibility
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911737427525632 |
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| author | Harlander, Jens Rosebrock, Stephan |
| author_facet | Harlander, Jens Rosebrock, Stephan |
| contents | If a complex $X$ is a subcomplex of a diagrammatically reducible 2-complex $Y$ that has locally indicable fundamental group, then $X$ has locally indicable fundamental group. This is a consequence of the Corson-Trace characterization of diagrammatic reducibility. In this paper we use a Corson-Trace like characterization of diagrammatic reducibility away from a subcomplex to obtain a considerable stronger result. We apply this to the question of local indicability in the context of Whitehead's asphericity conjecture. We show that an injective labeled oriented tree (LOT) that is diagrammatically reducible of degree 2, and all its quotients are as well, is locally indicable. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local indicability in the presence of diagrammatic reducibility Harlander, Jens Rosebrock, Stephan Geometric Topology Group Theory 57M07, 57M05, 20F05, 20F06, 20F65 If a complex $X$ is a subcomplex of a diagrammatically reducible 2-complex $Y$ that has locally indicable fundamental group, then $X$ has locally indicable fundamental group. This is a consequence of the Corson-Trace characterization of diagrammatic reducibility. In this paper we use a Corson-Trace like characterization of diagrammatic reducibility away from a subcomplex to obtain a considerable stronger result. We apply this to the question of local indicability in the context of Whitehead's asphericity conjecture. We show that an injective labeled oriented tree (LOT) that is diagrammatically reducible of degree 2, and all its quotients are as well, is locally indicable. |
| title | Local indicability in the presence of diagrammatic reducibility |
| topic | Geometric Topology Group Theory 57M07, 57M05, 20F05, 20F06, 20F65 |
| url | https://arxiv.org/abs/2511.15212 |