Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nielsen Realisation by Gluing: Limit Groups and Free Products   We generalise the Karrass-Pietrowski-Solitar and the Nielsen realisation
theorems from the setting of free groups to that of free products. As a result,
we obtain a fixed point theorem for finite groups of outer automorphisms acting
on the relative free splitting complex of Handel--Mosher and on the outer space
of a free product of Guirardel--Levitt, as well as a relative version of the
Nielsen realisation theorem, which in the case of free groups answers a
question of Karen Vogtmann. We also prove Nielsen realisation for limit groups,
and as a byproduct obtain a new proof that limit groups are CAT($0$). The
proofs rely on a new version of Stallings' theorem on groups with at least two
ends, in which some control over the behaviour of virtual free factors is
gained.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph