Goldman 符号形式在 $\mathrm{SL}(3,\mathbb R)$ Hitchin 构件上的复结构兼容性
微分几何
2025-06-16 v3 几何拓扑
摘要
我们证明了在 Hitchin 构件上，Goldman 符号形式与 Labourie-Loftin 复结构相容，二者共同决定了一个（映射类群不变的）伪 K"ahler 结构。
引用
@article{arxiv.2411.02350,
title = {Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component},
author = {Christian El Emam and Nathaniel Sagman},
journal= {arXiv preprint arXiv:2411.02350},
year = {2025}
}
备注
The main result has now been absorbed into a much larger work currently submitted to arXiv. As well, this paper cites and makes use of content from a previous version of the paper arXiv:2406.15287 that has since been removed. We plan to rewrite this paper and purpose it as an expository note