Talk page
Title:
Complete and conically singular G_2-manifolds of cohomogeneity one
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Abstract:
Bryant and Salmon's cohomogeneity 1 examples of complete, asymptotically conical G_2-manifolds provide a model for desingularising compact G_2-manifolds with conical singularities; however no examples of the latter are yet known, and there are also no further known examples of asymptotically conical G_2-manifolds. Theoretical physicists such as Cvetic-Gibbons-Lu-Pope and Brandhuber-Gomis-Gubser-Gukov have considered complete cohomogeneity 1 G_2-manifolds that are "asymptotically locally conical"--the model at infinity is a circle bundle over a cone--and which in a 1-parameter family converge to an asymptotically cylindrical manifold. However, only some of these families have been studied rigorously (Bazaikin-Bogoyavlenskaya). I will discuss joint work in progress with Foscolo and Haskins on these families, and some of their limits, which include a new asymptotically conical G_2-manifold and a conically singular G_2-manifold with locally conical asymptotics. The latter may provide an avenue to construction of compact G_2-manifolds with conical singularities.
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