Fortier Bourque, M. (2018) The holomorphic couch theorem. Inventiones Mathematicae, 212(2), pp. 319-406. (doi: 10.1007/s00222-017-0769-6)
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170406.pdf - Published Version Available under License Creative Commons Attribution. 1MB |
Abstract
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.
| Item Type: | Articles |
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| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Fortier-Bourque, Dr Maxime |
| Authors: | Fortier Bourque, M. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Inventiones Mathematicae |
| Journal Abbr.: | Invent. Math. |
| Publisher: | Springer |
| ISSN: | 0020-9910 |
| ISSN (Online): | 1432-1297 |
| Published Online: | 07 December 2017 |
| Copyright Holders: | Copyright © 2017 The Author |
| First Published: | First published in Inventiones Mathematicae 212(2): 319-406 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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