Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost commuting matrices, cohomology, and dimension   We investigate which relations for families of commuting matrices are stable
under small perturbations, or in other words, which commutative $C^*$-algebras
$C(X)$ are matricially semiprojective. Extending the works of Davidson,
Eilers-Loring-Pedersen, Lin and Voiculescu on almost commuting matrices, we
identify the precise dimensional and cohomological restrictions for
finite-dimensional spaces $X$ and thus obtain a complete characterization:
$C(X)$ is matricially semiprojective if and only if $\dim(X)\leq 2$ and
$H^2(X;\mathbb{Q})=0$. We give several applications to lifting problems for
commutative $C^*$-algebras, in particular to liftings from the Calkin algebra
and to $l$-closed $C^*$-algebras in the sense of Blackadar.

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The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an