Smooth and analytic actions of $SL(n,{\bf R})$ and $SL(n,{\bf Z})$ on closed $n$-dimensional manifolds

David Fisher; Karin Melnick

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arXiv · 2210.09516

Smooth and analytic actions of $SL(n,{\bf R})$ and $SL(n,{\bf Z})$ on closed $n$-dimensional manifolds

David Fisher·Karin Melnick

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Abstract

The main result is a classification of smooth actions of $SL(n,{\bf R})$, $n \geq 3$, or connected groups locally isomorphic to it, on closed $n$-manifolds, extending a theorem of Uchida. We construct new exotic actions of $SL(n,{\bf Z})$ on the $n$-torus and connected sums of $n$-tori, and we formulate a conjectural classification of actions of lattices in $SL(n,{\bf R})$ on closed $n$-manifolds. We prove some results about invariant rigid geometric structures for $SL(n,{\bf R})$-actions.

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BibTeX RIS

David Fisher, Karin Melnick. 2022-10-18. Smooth and analytic actions of $SL(n,{\bf R})$ and $SL(n,{\bf Z})$ on closed $n$-dimensional manifolds. https://arxiv.org/abs/2210.09516

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