2 problems

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Bing–Borsuk conjecture for homogeneous metric ANR-compacta
Bing–Borsuk conjecture. Every $n$ -dimensional homogeneous metric ANR-compactum is an $n$ -manifold.
Conjectureopenanr-spaces geometric-topology homogeneous-spacesarXiv posted 2 days ago
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Modified Bing–Borsuk conjecture for homogeneous ANR-spaces
Modified Bing–Borsuk conjecture. Every locally compact homogeneous $ANR$ -space of dimension $n\geq 3$ is a generalized $n$ -manifold.
Conjecturerefutedanr-spaces geometric-topology homogeneous-spacesarXiv posted 2 days ago

Bing–Borsuk conjecture for homogeneous metric ANR-compacta