Cartan actions of higher rank abelian groups and their classification.

Autor:	Spatzier, Ralf, Vinhage, Kurt
Předmět:	ABELIAN groups TOPOLOGICAL groups FOLIATIONS (Mathematics) CLASSIFICATION DIFFEOMORPHISMS LOGICAL prediction
Zdroj:	Journal of the American Mathematical Society; Jul2024, Vol. 37 Issue 3, p731-859, 129p
Abstrakt:	We study \mathbb {R}^k \times \mathbb {Z}^\ell actions on arbitrary compact manifolds with a projectively dense set of Anosov elements and 1-dimensional coarse Lyapunov foliations. Such actions are called totally Cartan actions. We completely classify such actions as built from low-dimensional Anosov flows and diffeomorphisms and affine actions, verifying the Katok-Spatzier conjecture for this class. This is achieved by introducing a new tool, the action of a dynamically defined topological group describing paths in coarse Lyapunov foliations, and understanding its generators and relations. We obtain applications to the Zimmer program. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
Externí odkaz:	Zobrazit plný text záznamu