\(L^2\)-cohomology of quasi-fibered boundary metrics (Q6536651)

The authors introduce the notion of quasi-fibered boundary metric, generalizing and intersecting a number of preceding definitions in the Riemannian setting, see in particular [\textit{T. Hausel} et al., Duke Math. J. 122, No. 3, 485--548 (2004; Zbl 1062.58002); \textit{E. Hunsicker} and \textit{F. Rochon} [Ann. Math. Qué. 39, No. 2, 177--184 (2015; Zbl 1331.58004)]. In this frame they are addressed to new results about Fredholm theory for elliptic operators and Hodge cohomology. Reference is given to the pseudo-differential calculus of the authors (arXiv: 2103.16650). Very interesting applications concern the metric of \textit{H. Nakajima} [Lectures on Hilbert schemes of points on surfaces. Providence, RI: American Mathematical Society (1999; Zbl 0949.14001)] and the proof of the comjecture of \textit{A. Sen} [Phys. Lett., B 329, No. 2--3, 217--221 (1994; Zbl 1190.81113)].