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Home » Postdoc Lunch Seminar I: Exotic nearly Kähler structures on the 6-sphere and the product of two 3-spheres

Seminar

Postdoc Lunch Seminar I: Exotic nearly Kähler structures on the 6-sphere and the product of two 3-spheres April 22, 2016 (11:30 AM PDT - 12:20 PM PDT)
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Location: MSRI: Simons Auditorium
Speaker(s) Lorenzo Foscolo (State University of New York, Stony Brook)
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Compact 6-dimensional nearly Kähler manifolds are the cross-sections of Riemannian cones with G2 holonomy. In particular they are Einstein manifolds with positive scalar curvature and admit real Killing spinors. Viewing Euclidean 7-space as the cone over the round 6-sphere endows the 6-sphere with a nearly Kähler structure which coincides with the standard G2-invariant almost complex structure induced by octonionic multiplication. A long-standing problem has been the question of existence of complete nearly Kähler 6-manifolds besides the four known homogeneous ones. We resolve this problem by proving the existence of an exotic (inhomogeneous) nearly Kähler structure on the 6-sphere and on the product of two 3-spheres. This is joint work with Mark Haskins, Imperial College London.



 

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