Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collapsing to Alexandrov spaces with isolated mild singularities   Let $M_j$ be a sequence of Riemannian manifolds with sectional curvature
bound below collapsing to a compact Alexandrov space $X$ of dimension $k$.
Suppose that all but finitely many points of $X$ are $(k,\delta)$-strained and
that the space of directions at each exceptional point contains $k+1$
directions making obtuse angles with each other. We prove that $M_j$ admits a
structure of locally trivial fibration over $X$ for sufficiently large $j$. The
same is true for collapsing sequences of Alexandrov spaces such that the
infimum of the volume of the spaces of directions is sufficiently large
relative to $\delta$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom