Quadratic Thurston maps with few postcritical points

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 few...

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Veröffentlicht in:	Geometriae dedicata 2019-08, Vol.201 (1), p.33-55
Hauptverfasser:	Kelsey, Gregory, Lodge, Russell
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebraic Geometry Combinatorial analysis Convex and Discrete Geometry Differential Geometry Enumeration Hyperbolic Geometry Mathematics Mathematics and Statistics Original Paper Projective Geometry Self-similarity Topology
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Zusammenfassung:	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.
ISSN:	0046-5755 1572-9168
DOI:	10.1007/s10711-018-0387-5