2008/07/31 by Spiro Karigiannis
Mathematics · #Conical surface #Geometric and Algebraic Topology #Geometry and complex manifolds #Gravitational singularity #Manifold (fluid mechanics) #Neighbourhood (mathematics) #Nonlinear Partial Differential Equations #Point (geometry) #Singular point of a curve #Singularity #math.AP #math.DG #msc:53C29 #msc:58J05
paper · pdf · doi:10.2140/gt.2009.13.1583
published as Geom. Topol. 13 (2009) 1583-1655 · 55 pages, 6 figures. Version 2: Corrected small error in the proof of Lemma 2.12. (The statement of the lemma has not changed.)
arxiv created 2008/10/23 · openalex publication_date 2009/03/03 · arxiv updated 2014/11/11 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
We present a method to desingularize a compact G 2 manifold M with isolated conical singularities by cutting out a neighbourhood of each singular point x i and gluing in an asymptotically conical G 2 manifold N i . Controlling the error on the overlap gluing region enables us to use a result of Joyce to conclude that the resulting compact smooth 7-manifold M admits a torsion-free G 2 structure, with full G 2 holonomy.