Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Definable Topological Dynamics of $SL_2(\mathbb{C}((t))$   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 $M = \mathbb{C}((t))$; 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 $\mathbb{C}((t))$. 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.

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The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
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The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat