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Presentations of NET maps

Volume 244 / 2019

William Floyd, Walter Parry, Kevin M. Pilgrim Fundamenta Mathematicae 244 (2019), 49-72 MSC: Primary 37F10; Secondary 57M12. DOI: 10.4064/fm351-11-2017 Published online: 16 July 2018


A branched covering $f\colon S^2 \to S^2$ is a nearly Euclidean Thurston (NET) map if each critical point is simple and its postcritical set has exactly four points. We show that up to equivalence, each NET map admits a normal form in terms of simple affine data. This data can then be used as input for algorithms developed for the computation of fundamental invariants, now systematically tabulated in a large census.


  • William FloydDepartment of Mathematics
    Virginia Tech
    Blacksburg, VA 24061, U.S.A.
  • Walter ParryDepartment of Mathematics
    Eastern Michigan University
    Ypsilanti, MI 48197, U.S.A.
  • Kevin M. PilgrimDepartment of Mathematics
    Indiana University
    Bloomington, IN 47405, U.S.A.

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