Corpus ID: 232428040

# $L^2$-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}
}
• Published 2021
• Mathematics, Physics
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

#### References

SHOWING 1-10 OF 48 REFERENCES
Asymptotic Geometry of the Hitchin Metric
• Mathematics, Physics
• 2017
AbstractWe study the asymptotics of the natural L2 metric on the Hitchin moduli space with group $${G = \mathrm{SU}(2)}$$G=SU(2). Our main result, which addresses a detailed conjectural picture madeExpand
L2-Cohomology of Hyperkähler Quotients
Abstract: Using an argument of Jost and Zuo, we give a criterion which implies that the L2 harmonic forms on a complete noncompact hyperkähler manifold lie in the middle dimension and are invariantExpand
Quasi-asymptotically conical Calabi-Yau manifolds
• Mathematics
• 2016
We construct new examples of quasi-asymptotically conical (QAC) Calabi-Yau manifolds that are not quasi-asymptotically locally Euclidean (QALE). We do so by first providing a natural compactificationExpand
Vanishing of intersection numbers on the moduli space of Higgs bundles
In this paper we consider the topological side of a problem which is the analogue of Sen's S-duality testing conjecture for Hitchin's moduli space of rank 2 stable Higgs bundles of fixed determinantExpand
The cohomology of the space of magnetic monopoles
• Mathematics
• 1996
Denote byXq the reduced space ofSU2 monopoles of chargeq in ℝ3. In this paper the cohomology ofXq, the cohomology with compact supports ofXq, and the image of the latter in the former are allExpand
Lectures on Hilbert schemes of points on surfaces
Introduction Hilbert scheme of points Framed moduli space of torsion free sheaves on $\mathbb{P}^2$ Hyper-Kahler metric on $(\mathbb{C}^2)^{[n]}$ Resolution of simple singularities PoincareExpand
The signature package on Witt spaces
• Physics, Mathematics
• 2011
In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratifiedExpand
Weighted Hodge cohomology of iterated fibred cusp metrics
• Mathematics
• 2015
On a smoothly stratified space, we identify intersection cohomology of any given perversity with an associated weighted $$L^2$$L2 cohomology for iterated fibred cusp metrics on the smoothExpand
The McKay correspondence for finite subgroups of SL(3,\C)
• Mathematics
• 1994
This is the final draft, containing very minor proof-reading corrections. Let G in SL(n,\C) be a finite subgroup and \fie: Y -> X = \C^n/G any resolution of singularities of the quotient space. WeExpand
Pseudodifferential operators on manifolds with fibred corners
• Mathematics
• 2011
One way to geometrically encode the singularities of a stratified pseudomanifold is to endow its interior with an iterated fibred cusp metric. For such a metric, we develop and study aExpand