Thurston's pullback map on the augmented Teichmuller space and applications

• 成果类型: Article
• 署名作者: Selinger, Nikita
• 署名单位: Constructor University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0362-3
• 发表日期: 2012
• 页码: 111-142
• 关键词: riemann surfaces; geometry

摘要

Let f be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map sigma (f) of a finite-dimensional Teichmuller space. We prove that this map extends continuously to the augmented Teichmuller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichmuller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.