Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic mapping class groups of Cantor manifolds and their finiteness
  properties   A Cantor manifold $\mathcal C$ is a non-compact manifold obtained by gluing
(holed) copies of a fixed compact manifold $Y$ in a tree-like manner.
Generalizing classical families of groups due to Brin, Dehornoy, and Funar-
Kapoudjian, we introduce the asymptotic mapping class group $\mathcal B$ of
$\mathcal C$, whose elements are proper isotopy classes of self-diffeomorphisms
of $\mathcal C$ that are eventually trivial. The group $\mathcal B$ happens to
be an extension of a Higman-Thompson group by a direct limit of mapping class
groups of compact submanifolds of $\mathcal C$.
  We construct an infinite-dimensional contractible cube complex $\mathfrak X$
on which $\mathcal B$ acts. For certain well-studied families of manifolds, we
prove that $\mathcal B$ is of type $F_\infty$ and that $\mathfrak X$ is ${\rm
CAT}(0)$; more concretely, our methods apply for example when $Y$ is
diffeomorphic to $\mathbb S^1 \times \mathbb S^1$, $\mathbb S^2\times \mathbb
S^1$, or $\mathbb S^n \times \mathbb S^n$ for $n\ge 3$. In these cases,
$\mathcal B$ contains, respectively, the mapping class group of every compact
surface with boundary; the automorphism group of the free group on $k$
generators for all $k$; and an infinite family of (arithmetic) symplectic or
orthogonal groups.
  In particular, if $Y \cong \mathbb S^2$ or $ \mathbb S^1 \times \mathbb S^1$,
our result gives a positive answer to a question of
Funar--Kapoudjian--Sergiescu. In addition, for $Y\cong \mathbb S^1 \times
\mathbb S^1$ or $ \mathbb S^2\times \mathbb S^1$, the homology of $\mathcal B$
coincides with the stable homology of the relevant mapping class groups, as
studied by Harer and Hatcher--Wahl.

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The categories of this paper are: ao-sci
18
The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an