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arXiv · 2411.02350

Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component

Christian El Emam·Nathaniel Sagman
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Abstract

We prove that, on the $\mathrm{SL}(3,\mathbb R)$ 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.

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Christian El Emam, Nathaniel Sagman. 2024-11-04. Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component. https://arxiv.org/abs/2411.02350

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