$L^2$-cohomology of quasi-fibered boundary metrics
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866911824680583168 |
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| author | Kottke, Chris Rochon, Frédéric |
| author_facet | Kottke, Chris Rochon, Frédéric |
| contents | We develop new techniques to compute the weighted $L^2$-cohomology of quasi-fibered boundary metrics (QFB-metrics). Combined with the decay of $L^2$-harmonic forms obtained in a companion paper, this allows us to compute the reduced $L^2$-cohomology for various classes of QFB-metrics. Our results applies in particular to the Nakajima metric on the Hilbert scheme of $n$ points on $\mathbb{C}^2$, for which we can show that the Vafa-Witten conjecture holds. Using the compactification of the monopole moduli space announced by Fritzsch, the first author and Singer, we can also give a proof of the Sen conjecture for the monopole moduli space of magnetic charge 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_16655 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | $L^2$-cohomology of quasi-fibered boundary metrics Kottke, Chris Rochon, Frédéric Differential Geometry Mathematical Physics Geometric Topology 58J10, 55N33 We develop new techniques to compute the weighted $L^2$-cohomology of quasi-fibered boundary metrics (QFB-metrics). Combined with the decay of $L^2$-harmonic forms obtained in a companion paper, this allows us to compute the reduced $L^2$-cohomology for various classes of QFB-metrics. Our results applies in particular to the Nakajima metric on the Hilbert scheme of $n$ points on $\mathbb{C}^2$, for which we can show that the Vafa-Witten conjecture holds. Using the compactification of the monopole moduli space announced by Fritzsch, the first author and Singer, we can also give a proof of the Sen conjecture for the monopole moduli space of magnetic charge 3. |
| title | $L^2$-cohomology of quasi-fibered boundary metrics |
| topic | Differential Geometry Mathematical Physics Geometric Topology 58J10, 55N33 |
| url | https://arxiv.org/abs/2103.16655 |