We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Infinitely many new families of complete cohomogeneity one G<sub>2</sub>-manifolds: G<sub>2</sub> analogues of the Taub-NUT and Eguchi-Hanson spaces.
- Authors
Foscolo, Lorenzo; Haskins, Mark; Nordström, Johannes
- Abstract
We construct infinitely many new 1-parameter families of simply connected complete non-compact G2-manifolds with controlled geometry at infinity. The generic member of each family has so-called asymptotically locally conical (ALC) geometry. However, the nature of the asymptotic geometry changes at two special parameter values: at one special value we obtain a unique member of each family with asymptotically conical (AC) geometry; on approach to the other special parameter value the family of metrics collapses to an AC Calabi-Yau 3-fold. Our infinitely many new diffeomorphism types of AC G2-manifolds are particularly noteworthy: previously the three examples constructed by Bryant and Salamon in 1989 furnished the only known simply connected AC G2-manifolds. We also construct a closely related conically singular G2-holonomy space: away from a single isolated conical singularity, where the geometry becomes asymptotic to the G2-cone over the standard nearly Kähler structure on the product of a pair of 3-spheres, the metric is smooth and it has ALC geometry at infinity. We argue that this conically singular ALC G2-space is the natural G2 analogue of the Taub-NUT metric in 4-dimensional hyperKähler geometry and that our new AC G2-metrics are all analogues of the Eguchi-Hanson metric, the simplest ALE hyperKähler manifold. Like the Taub-NUT and Eguchi-Hanson metrics, all our examples are cohomogeneity one, i.e. they admit an isometric Lie group action whose generic orbit has codimension one.
- Subjects
MANIFOLDS (Mathematics); DIFFEOMORPHISMS; HOLONOMY groups; LIE groups; DIMENSION theory (Algebra)
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2021, Vol 23, Issue 7, p2153
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1051