A new construction of compact torsion-free \(G_2\)-manifolds by gluing families of Eguchi-Hanson spaces

DOI10.4310/jdg/1612975017zbMath1464.53067arXiv1707.09325OpenAlexW2884257857WikidataQ115164522 ScholiaQ115164522MaRDI QIDQ2228092

Spiro Karigiannis, Dominic David Joyce

Publication date: 16 February 2021

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.09325

zbMATH Keywords

Calabi-Yau 3-foldsresolution\(G_2\)-structures\(G_2\)-involutions\(G_2\)-orbifoldtorsion-free \(G_2\)-structures

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Issues of holonomy in differential geometry (53C29)

Related Items

A compact \(\mathrm G_2\)-calibrated manifold with first Betti number \(b_1 = 1\), A construction of \(G_2\)-manifolds from K3 surfaces with a \(\mathbb{Z}_2^2\)-action, A new complete Calabi-Yau metric on \({\mathbb {C}}^3\), Closed \({G_2}\)-structures on compact quotients of Lie groups, A compact non‐formal closed G₂manifold with b1=1$b_1=1$, \(G_2\)-instantons on resolutions of \(G_2\)-orbifolds, Harmonic \(\operatorname{G}_2\)-structures on almost abelian Lie groups, Associative submanifolds in Joyce's generalised Kummer constructions, Exact \(\mathrm{G}_2\)-structures on compact quotients of Lie groups, Coulomb and Higgs phases of \(G_2\)-manifolds, K3 surfaces with two involutions and low Picard number, Constructions of Compact $$G_2$$-Holonomy Manifolds, Eleven-dimensional supergravity in 4D, \(N=1\) superspace, A class of eternal solutions to the G\(_2\)-Laplacian flow, On mirror maps for manifolds of exceptional holonomy, Explicit soliton for the Laplacian co-flow on a solvmanifold, Local \(G_2\)-manifolds, Higgs bundles and a colored quantum mechanics, New \(G_2\)-conifolds in \(M\)-theory and their field theory interpretation, The Laplacian flow of locally conformal calibrated \(\operatorname{G}_{2}\)-structures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotically cylindrical Calabi-Yau 3-folds from weak Fano 3-folds
• \(G_{2}\)-instantons on generalised Kummer constructions
• \(G_2\)-manifolds and associative submanifolds via semi-Fano 3-folds
• New invariants of \(G_{2}\)-structures
• Desingularization of \(G_{2}\) manifolds with isolated conical singularities
• Calibrated geometries
• A new proof of the existence of Kähler-Einstein metrics on K3. I
• The construction of ALE spaces as hyper-Kähler quotients
• Self-dual solutions to Euclidean gravity
• Ricci-flat metrics on the complexification of a compact rank one symmetric space
• Large complex structure limits of \(K3\) surfaces
• On the construction of some complete metrics with exceptional holonomy
• Factor groups of groups of automorphisms of hyperbolic forms with respect to subgroups generated by 2-reflections. Algebro-geometric applications
• Compact Riemannian 7-manifolds with holonomy \(G_ 2\). I
• Compact Riemannian 7-manifolds with holonomy \(G_ 2\). II
• Mirror symmetry is \(T\)-duality
• Deformation theory of \(\mathrm{G}_2\) conifolds
• Del Pezzo and \(K3\) surfaces
• Gauge Theory in higher dimensions, II
• K3 surfaces with non-symplectic involution and compact irreducible G₂-manifolds
• FLOWS OF G2-STRUCTURES, I
• Fredholm, Hodge and Liouville Theorems on Noncompact Manifolds
• Métriques kählériennes et fibrés holomorphes
• Twisted connected sums and special Riemannian holonomy