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

@inproceedings{Kottke2021L2cohomologyOQ, title={\$L^2\$-cohomology of quasi-fibered boundary metrics}, author={C. Kottke and Fr'ed'eric Rochon}, year={2021} }

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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