Corpus ID: 232428040

$L^2$-cohomology of quasi-fibered boundary metrics

  title={\$L^2\$-cohomology of quasi-fibered boundary metrics},
  author={C. Kottke and Fr'ed'eric Rochon},
We develop new techniques to compute the weighted L-cohomology of quasi-fibered boundary metrics (QFB-metrics). Combined with the decay of L-harmonic forms obtained in a companion paper, this allows us to compute the reduced L-cohomology for various classes of QFB-metrics. Our results applies in particular to the Nakajima metric on the Hilbert scheme of 4 points on C, for which we can show that the Vafa-Witten conjecture holds. Using the compactification of the monopole moduli space announced… Expand


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