Local rigidity of weak or no hyperbolicity algebraic actions

Wang, Zhenqi

doi:10.1090/jams/1058

Local rigidity of weak or no hyperbolicity algebraic actions
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by Zhenqi Jenny Wang;

J. Amer. Math. Soc.

DOI: https://doi.org/10.1090/jams/1058

Published electronically: April 9, 2025

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Abstract:

In this paper we study rigidity properties of abelian \hyphenation{break-able}actions with weak or no hyperbolicity. We introduce a general strategy for proving $C^\infty$ local rigidity of algebraic actions. As a consequence, we show $C^\infty$ local rigidity for a broad class of parabolic algebraic actions on homogeneous spaces of semisimple Lie groups. This is the first time in the literature that (strong) local rigidity for these actions is addressed.

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Local rigidity of weak or no hyperbolicity algebraic actions
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Abstract: