Hodge cohomology of gravitational instantons
| dc.creator | Hausel, Tamas | |
| dc.creator | Hunsicker, Eugenie | |
| dc.creator | Mazzeo, Rafe | |
| dc.date | 2002-07-19 | |
| dc.date | 2003-08-05 | |
| dc.date.accessioned | 2026-07-07T04:49:45Z | |
| dc.date.available | 2026-07-07T04:49:45Z | |
| dc.description | 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 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 [dai] and more generally by Vaillant [Va], 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 [Car] and the forthcoming paper of Cheeger and Dai [CD]. 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. | |
| dc.description | 45 pages; corrected final version. To appear in Duke Math. Journal | |
| dc.identifier | https://arxiv.org/abs/math/0207169 | |
| dc.identifier | http://arxiv.org/abs/math/0207169 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64546 | |
| dc.subject | Differential Geometry | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Mathematical Physics | |
| dc.subject | 58A14, 32S60 | |
| dc.title | Hodge cohomology of gravitational instantons | |
| dc.type | text |