Dynamical Systems Seminar | Miri Son (Rice University)

Title: Classification of SL(n,R)-actions on closed manifolds

Abstract: Recently, Fisher and Melnick classified SL(n,R)-actions on n-dimensional manifolds for n≥3. In this talk, we generalize this result by classifying smooth or real-analytic SL(n,R)-actions on m-dimensional manifolds for 3≤n≤m≤2n-3. This work is motivated by the Zimmer program and is central to it, as Lie group actions restrict to their lattice actions. 

This classification relies on the linearization of SL(n,R)-actions when there is a global fixed point. The analytic case was proved by Guillemin—Sternberg and Kushinirenko. We discuss the smooth case which is ongoing joint work with Insung Park.

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