Foscolo, L;
(2021)
Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds.
Geometry and Topology
, 25
(1)
pp. 339-408.
10.2140/gt.2021.25.339.
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Abstract
We present an analytic construction of complete non-compact 8-dimensional Ricci-flat manifolds with holonomy Spin(7). The construction relies on the study of the adiabatic limit of metrics with holonomy Spin(7) on principal Seifert circle bundles over asymptotically conical G2 orbifolds. The metrics we produce have an asymptotic geometry, so-called ALC geometry, that generalises to higher dimensions the geometry of 4-dimensional ALF hyperk\"ahler metrics. We apply our construction to asymptotically conical G2 metrics arising from self-dual Einstein 4-orbifolds with positive scalar curvature. As illustrative examples of the power of our construction, we produce complete non-compact Spin(7) manifolds with arbitrarily large second Betti number and infinitely many distinct families of ALC Spin(7) metrics on the same smooth 8-manifold.
| Type: | Article |
|---|---|
| Title: | Complete non-compact Spin(7) manifolds from self-dual Einstein 4-orbifolds |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/gt.2021.25.339 |
| Publisher version: | https://doi.org/10.2140/gt.2021.25.339 |
| Language: | English |
| Additional information: | This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10093207 |
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