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Abstract:

We initiate a study of definable topological dynamics for groups definable in metastable theories. Specifically, we consider the special linear group G = SL_2 with entries from M = ℂ((t)); the field of formal Laurent series with complex coefficients. We prove such a group is not definably amenable, find a suitable group decomposition, and describe the minimal flows of the additive and multiplicative groups of ℂ((t)). The main result is an explicit description of the minimal flow and Ellis Group of (G(M),S_G(M)) and we observe that this is not isomorphic to G/G^{00}, answering a question as to whether metastability is a suitable weakening of a conjecture of Newelski.

Mathematics Subject Classification: 54H20, 03C98

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Full text arXiv 1903.03570: pdf, ps.