---
OA_place: repository
OA_type: green
_id: '1456'
abstract:
- lang: eng
  text: We study the space of L2 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 L2 signature formula implied by our result is closely related
    to the one proved by Dai and more generally by Vaillant and identifies Dai's τ-invariant
    directly in terms of intersection cohomology of differing perversities. This work
    is also closely related to a recent paper of Carron and the forthcoming paper
    of Cheeger and Dai. We apply our results to a number of examples, gravitational
    instantons among them, arising in predictions about L2 harmonic forms in duality
    theories in string theory.
acknowledgement: "Hausel’s work supported by a Miller Research Fellowship at the University
  of California, Berkeley.\r\nHunsicker’s work partially supported by Stanford University.\r\nMazzeo’s
  work supported by National Science Foundation grant numbers DMS-991975 and DMS-0204730
  and\r\nby the Mathematical Sciences Research Institute."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Tamas
  full_name: Hausel, Tamas
  id: 4A0666D8-F248-11E8-B48F-1D18A9856A87
  last_name: Hausel
  orcid: 0000-0002-9582-2634
- first_name: Eugénie
  full_name: Hunsicker, Eugénie
  last_name: Hunsicker
- first_name: Rafe
  full_name: Mazzeo, Rafe
  last_name: Mazzeo
citation:
  ama: Hausel T, Hunsicker E, Mazzeo R. Hodge cohomology of gravitational instantons.
    <i>Duke Mathematical Journal</i>. 2004;122(3):485-548. doi:<a href="https://doi.org/10.1215/S0012-7094-04-12233-X">10.1215/S0012-7094-04-12233-X</a>
  apa: Hausel, T., Hunsicker, E., &#38; Mazzeo, R. (2004). Hodge cohomology of gravitational
    instantons. <i>Duke Mathematical Journal</i>. Duke University Press. <a href="https://doi.org/10.1215/S0012-7094-04-12233-X">https://doi.org/10.1215/S0012-7094-04-12233-X</a>
  chicago: Hausel, Tamás, Eugénie Hunsicker, and Rafe Mazzeo. “Hodge Cohomology of
    Gravitational Instantons.” <i>Duke Mathematical Journal</i>. Duke University Press,
    2004. <a href="https://doi.org/10.1215/S0012-7094-04-12233-X">https://doi.org/10.1215/S0012-7094-04-12233-X</a>.
  ieee: T. Hausel, E. Hunsicker, and R. Mazzeo, “Hodge cohomology of gravitational
    instantons,” <i>Duke Mathematical Journal</i>, vol. 122, no. 3. Duke University
    Press, pp. 485–548, 2004.
  ista: Hausel T, Hunsicker E, Mazzeo R. 2004. Hodge cohomology of gravitational instantons.
    Duke Mathematical Journal. 122(3), 485–548.
  mla: Hausel, Tamás, et al. “Hodge Cohomology of Gravitational Instantons.” <i>Duke
    Mathematical Journal</i>, vol. 122, no. 3, Duke University Press, 2004, pp. 485–548,
    doi:<a href="https://doi.org/10.1215/S0012-7094-04-12233-X">10.1215/S0012-7094-04-12233-X</a>.
  short: T. Hausel, E. Hunsicker, R. Mazzeo, Duke Mathematical Journal 122 (2004)
    485–548.
date_created: 2018-12-11T11:52:08Z
date_published: 2004-04-15T00:00:00Z
date_updated: 2026-09-30T13:26:24Z
day: '15'
doi: 10.1215/S0012-7094-04-12233-X
extern: '1'
external_id:
  arxiv:
  - '0207169'
fulldoi: https://doi.org/10.1215/S0012-7094-04-12233-X
intvolume: '       122'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/math/0207169
month: '04'
oa: 1
oa_version: None
page: 485 - 548
publication: Duke Mathematical Journal
publication_identifier:
  eissn:
  - 1547-7398
  issn:
  - 0012-7094
publication_status: published
publisher: Duke University Press
publist_id: '5737'
status: public
title: Hodge cohomology of gravitational instantons
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 122
year: '2004'
...