We study the structure of noncollapsed Gromov-Hausdorff limits of sequences, Min, of riemannian manifolds with special holonomy. We show that these spaces are smooth manifolds with special holonomy off a closed subset of codimension ≥4. Additional results on the the detailed structure of the singular set support our main conjecture that if the M in are compact and a certain characteristic number, C(Min), is bounded independent of i, then the singularities are of orbifold type off a subset of real codimension at least 6.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics