Publications [#345589] of Mark Haskins

Papers Published

1. Foscolo, L; Haskins, M, New G2-holonomy cones and exotic nearly Kahler structures on S⁶ and S³ x S³, Annals of Mathematics, vol. 185 no. 1 (January, 2017), pp. 59-130 [doi]
   (last updated on 2024/04/18)

   Abstract:
   There is a rich theory of so-called (strict) nearly Kahler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kahler 6-manifolds play a distinguished role both in the general structure theory and also because of their connection with singular spaces with holonomy group the compact exceptional Lie group G2: The metric cone over a Riemannian 6-manifold M has holonomy contained in G2 if and only if M is a nearly Kahler 6-manifold. A central problem in the field has been the absence of any complete inhomogeneous examples. We prove the existence of the first complete inhomogeneous nearly Kahler 6-manifolds by proving the existence of at least one cohomogeneity one nearly Kahler structure on the 6-sphere and on the product of a pair of 3-spheres. We conjecture that these are the only simply connected (inhomogeneous) cohomogeneity one nearly Kahler structures in six dimensions.