Differential Geometry: "Positive curvature in dimension 7"
Owen Dearricott, UC Riverside
Friday, November 3, 2017
11:10 a.m.–Noon
Location: Surge Building 268
Parking Information
Category: Seminar
Description:
In their 2008 paper Grove, Wilking and Ziller proposed two infinite families, P_k and Q_k where k>1, of simply connected manifolds in dimension 7 that may carry Riemannian metrics with positive curvature whose isometry groups' principal orbits are hypersurfaces. The two families occur as double covers of certain 3Sasakian manifolds given by the total spaces of the Konishibundles of certain selfdual Einstein metrics on orbifold 4spheres described by Hitchin in the early 90s. To date only one of these proposed candidates, P_2, is known to actually carry a metric with positive sectional curvature and the techniques employed in that case do not directly generalise to the series of candidates.
In this talk we discuss a promising new technique that should work to put positive curvature on the two series as it applies to the candidates Q_2 and P_3.
Additional Information: Math Seminars
Open to: General Public
Admission: Free
Sponsor: Mathematics
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