Abstract

AbstractReal analytic actions of connected Lie groups locally isomorphic to SL (2, ℝ) on compact surfaces, possibly with boundary, are classified up to topological conjugacy and up to real analytic conjugacy. Finite dimensional universal unfoldings of the real analytic conjugacy relation are also constructed. These are local transversals to the conjugacy classes in the space of actions. Sometimes the unfolding is a variety but not a manifold, and thus the space of actions is not naturally modelled on a vector space. We find many rigid actions and some unexpected bifurcation.

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