The Finite Global Attractor Conjecture holds for rational maps obtained by gluing two PCF polynomials, established by showing that intersection numbers with a finite set of separating arcs decay under pullback to attract all non-peripheral curves.
Hlushchanka,Tischler graphs of critically fixed rational maps and their applica- tions, preprint
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On the Global Curve Attractor for polynomial gluing
The Finite Global Attractor Conjecture holds for rational maps obtained by gluing two PCF polynomials, established by showing that intersection numbers with a finite set of separating arcs decay under pullback to attract all non-peripheral curves.