On homology of complements of compact sets in Hilbert Cube
  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. 
Ashwini Amarasinghe and Alexander Dranishnikov
math.GN math.AT