The holomorphic couch theorem

• 成果类型: Article
• 署名作者: Bourque, Maxime Fortier
• 署名单位: University of Toronto
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0769-6
• 发表日期: 2018
• 页码: 319-406
• 关键词: riemann surfaces; quadratic-differentials; teichmuller-spaces; EMBEDDINGS; foliations

摘要

We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy class is homotopy equivalent to a point, a circle, a torus, or the unit tangent bundle of the codomain, depending on the induced homomorphism on fundamental groups. Quadratic differentials play a central role in the proof.