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arXiv · 1603.00452

On homology of complements of compact sets in Hilbert Cube

Ashwini Amarasinghe·Alexander Dranishnikov
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Abstract

We introduce the notion of spaces with weak relative cohomology and show the acyclicity of the complement $Q\setminus X$ in the Hilbert cube $Q$ of a compactum $X$ with weak relative cohomology. As a corollary we obtain the acyclicity of the complement results when (a) $X$ is weakly infinite dimensional; (b) $X$ has finite cohomological dimension.

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Ashwini Amarasinghe, Alexander Dranishnikov. 2016-03-01. On homology of complements of compact sets in Hilbert Cube. https://arxiv.org/abs/1603.00452

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