Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component
Differential Geometry
2025-06-16 v3 Geometric Topology
Abstract
We prove that, on the Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (mapping class group invariant) pseudo-K\"ahler structure.
Keywords
Cite
@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}
}
Comments
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