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I know that G. Yu asked the question whether the universal cover of a closed aspherical manifold has finite asymptotic dimension in his Annals paper published in 1998. Was this question asked before?

  • About which definition of asymptotic dimension are we talking? The only one I know is a quasi-isometry invariant and so every compact manifold has asdim = 0. – AlexE Apr 27 '11 at 15:52
  • I meant the universal cover of the compact manifold, of course. For some reason, people forget "universal cover" and I got used to this bad habit. –  Apr 27 '11 at 17:04
  • Is your question about the existence of a closed aspherical manifold whose universal cover has infinite asymptotic dimension? Or just the historical issue of when this question was first asked? – Tom Church Apr 27 '11 at 17:09
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    I know the answer about existence. I proved it, the paper is in the arXiv: http://front.math.ucdavis.edu/1103.3873. I wanted to know if anybody before G. Yu formulated the question. I needed the answer for that paper. –  Apr 27 '11 at 17:21

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