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Quadratic Thurston maps with few postcritical points

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Abstract

We use the theory of self-similar groups to enumerate all combinatorial classes of non-Euclidean quadratic Thurston maps with fewer than five postcritical points. The enumeration relies on our computation that the corresponding maps on moduli space can be realized by quadratic rational maps with fewer than four postcritical points.

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Acknowledgements

Both authors gratefully acknowledge the support of the AIM SQuaRE Program 2013–2015. The second author was also supported by the Deutsche Forschungsgemeinschaft. The authors also thank Kevin Pilgrim, Walter Parry, and the anonymous referee for their helpful comments on early drafts of this article. Sarah Koch and Bill Floyd provided valuable perspectives and assistance, and the authors thank them as well.

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Authors and Affiliations

  1. Department of Mathematics, Bellarmine University, 2001 Newburg Rd, Louisville, KY, 40205, USA

    Gregory Kelsey

  2. Department of Mathematics and Computer Science, Indiana State University, Terre Haute, IN, 47809, USA

    Russell Lodge

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  1. Gregory Kelsey
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  2. Russell Lodge
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Correspondence to Gregory Kelsey.

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Kelsey, G., Lodge, R. Quadratic Thurston maps with few postcritical points. Geom Dedicata 201, 33–55 (2019). https://doi.org/10.1007/s10711-018-0387-5

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  • DOI: https://doi.org/10.1007/s10711-018-0387-5

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