Translator Disclaimer
2021 Complete noncompact Spin(7) manifolds from self-dual Einstein $4$–orbifolds
Lorenzo Foscolo
Geom. Topol. 25(1): 339-408 (2021). DOI: 10.2140/gt.2021.25.339

Abstract

We present an analytic construction of complete noncompact 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 hyperkähler 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 noncompact 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.

Citation

Download Citation

Lorenzo Foscolo. "Complete noncompact Spin(7) manifolds from self-dual Einstein $4$–orbifolds." Geom. Topol. 25 (1) 339 - 408, 2021. https://doi.org/10.2140/gt.2021.25.339

Information

Received: 5 April 2019; Revised: 20 December 2019; Accepted: 17 February 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/gt.2021.25.339

Subjects:
Primary: 53C25
Secondary: 53C10, 53C29, 53C80

Rights: Copyright © 2021 Mathematical Sciences Publishers

JOURNAL ARTICLE
70 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.25 • No. 1 • 2021
MSP
Back to Top