Iterated monodromy group of a PCF quadratic non-polynomial map
Manuscripta Mathematica, cilt.175, sa.1-2, ss.561-590, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 175 Sayı: 1-2
- Basım Tarihi: 2024
- Doi Numarası: 10.1007/s00229-024-01549-z
- Dergi Adı: Manuscripta Mathematica
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.561-590
- Anahtar Kelimeler: 11G32, 12F10, 37P05, 37P15
- Boğaziçi Üniversitesi Adresli: Evet
Özet
We study the postcritically finite non-polynomial map f(x)=1(x-1)2 over a number field k and prove various results about the geometric Ggeom(f) and arithmetic Garith(f) iterated monodromy groups of f. We show that the elements of Ggeom(f) are the ones in Garith(f) that fix certain roots of unity by assuming a conjecture on the size of Gngeom(f). Furthermore, we describe exactly for which a∈k the Arboreal Galois group Ga(f) and Garith(f) are equal.