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• W2017070602 abstract "We study the space of $L^2$ harmonic forms on complete manifolds with metrics of fibred boundary or fibred cusp type. These metrics generalize the geometric structures at infinity of several different well-known classes of metrics, including asymptotically locally Euclidean manifolds, the (known types of) gravitational instantons, and also Poincaré metrics on $mathbb{Q}$-rank $1$ ends of locally symmetric spaces and on the complements of smooth divisors in Kähler manifolds. The answer in all cases is given in terms of intersection cohomology of a stratified compactification of the manifold. The $L^2$ signature formula implied by our result is closely related to the one proved by Dai [25] and more generally by Vaillant [67], and identifies Dai's $tau$-invariant directly in terms of intersection cohomology of differing perversities. This work is also closely related to a recent paper of Carron [12] and the forthcoming paper of Cheeger and Dai [17]. We apply our results to a number of examples, gravitational instantons among them, arising in predictions about $L^2$ harmonic forms in duality theories in string theory." @default.
• W2017070602 created "2016-06-24" @default.
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• W2017070602 date "2004-04-15" @default.
• W2017070602 modified "2023-09-28" @default.
• W2017070602 title "Hodge cohomology of gravitational instantons" @default.
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• W2017070602 doi "https://doi.org/10.1215/s0012-7094-04-12233-x" @default.
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