Real analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds

Miri Son

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arXiv · 2508.04499

Real analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds

Miri Son

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Abstract

We classify real-analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds of dimension m for $3\leq n\leq m\leq2n-3$, which extends Fisher--Melnick's work for $\mathrm{SL}(n,\mathbb{R})$-actions on closed n-manifolds. Additionally, we classify smooth $\mathrm{SL}(n,\mathbb{R})$-actions on closed m-manifolds that are fixed-point free. As a corollary, we obtain the density or non-density of structural stability of fixed-point free $\mathrm{SL}(n,\mathbb{R})$-actions.

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Miri Son. 2025-08-06. Real analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds. https://arxiv.org/abs/2508.04499

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