PreprintarXiv licencearXiv
Holonomies of hyperbolic surfaces with one branch point
Abstract
Let S be a closed oriented surface of genus g≥ 2. We prove that any representation of π1(S) into PSL(2,ℝ) with Euler class 3−2g is the holonomy of a hyperbolic metric on S with one simple branch point.
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BibTeX
@misc{deroin2026holonomies,
title = {{Holonomies of hyperbolic surfaces with one branch point}},
author = {Bertrand Deroin and Nicolas Tholozan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42079},
eprint = {2610.42079},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42079},
}
RIS
TY - UNPB
TI - Holonomies of hyperbolic surfaces with one branch point
AU - Bertrand Deroin
AU - Nicolas Tholozan
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42079
UR - https://arxiv.org/abs/2610.42079
AB - Let S be a closed oriented surface of genus g≥ 2. We prove that any representation of π_1(S) into PSL(2,ℝ) with Euler class 3−2g is the holonomy of a hyperbolic metric on S with one simple branch point.
ER -