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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Bibliographic Details
Published in:Geometriae dedicata 2019-08, Vol.201 (1), p.33-55
Main Authors: Kelsey, Gregory, Lodge, Russell
Format: Article
Language:English
Subjects:
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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Summary: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