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Injective labeled oriented trees are aspherical

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Abstract

A labeled oriented tree is called injective, if each vertex occurs at most once as an edge label. We show that injective labeled oriented trees are aspherical. The proof uses a new relative asphericity test based on a lemma of Stallings.

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Notes

  1. We thank Manuela Ana Cerdeiro for pointing this example out to us.

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Authors and Affiliations

  1. Boise State University, Boise, ID, USA

    Jens Harlander

  2. Pädagogische Hochschule Karlsruhe, Karlsruhe, Germany

    Stephan Rosebrock

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  1. Jens Harlander
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  2. Stephan Rosebrock
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Correspondence to Stephan Rosebrock.

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Harlander, J., Rosebrock, S. Injective labeled oriented trees are aspherical. Math. Z. 287, 199–214 (2017). https://doi.org/10.1007/s00209-016-1823-6

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  • DOI: https://doi.org/10.1007/s00209-016-1823-6

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