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Global topology of hyperbolic components: Cantor circle case
Author(s) -
Wang Xiaoguang,
Yin Yongcheng
Publication year - 2017
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12058
Subject(s) - mathematics , moduli space , riemann surface , pure mathematics , locus (genetics) , quotient , teichmüller space , topology (electrical circuits) , combinatorics , biochemistry , chemistry , gene
We prove that in the moduli space M d of degree d ⩾ 2 rational maps, any hyperbolic component in the disconnectedness locus and of Cantor circle type is a finite quotient ofR 4 d − 4 − n × T n , where n is determined by dynamics. The proof uses some ideas from Riemann surface theory (Abel's Theorem), dynamical system and algebraic topology.