Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local cohomological properties of homogeneous ANR compacta   In accordance with the Bing-Borsuk conjecture, we show that if X is an
n-dimensional homogeneous metric ANR compactum and x\in X, then there is a
local basis at x consisting of connected open sets U such that the
cohomological properties of \overline U and bdU are similar to the properties
of the closed ball \mathbb B^n\subset\mathbb R^n and its boundary \mathbb
S^{n-1}. We also prove that a metric ANR compactum X of dimension n is
dimensionally full-valued if and only if the group H_n(X,X\setminus x) is not
trivial for some x\in X. This implies that every 3-dimensional homogeneous
metric ANR compactum is dimensionally full-valued.

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The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
14
The categories of this paper are: math-ph