Rod Gover - Geometric Compactification, Cartan holonomy, and asymptotics
Résumé
Conformal compactification has long been recognised as an effective geometric framework for relating conformal geometry, and associated field theories « at infinity », to the asymptotic phenomena of an interior (pseudo‐)‐Riemannian geometry of one higher dimension. It provides an effective approach for analytic problems in GR, geometric scattering, conformal invariant theory, as well as the AdS/CFT correspondence of Physics. I will describe how the notion of conformal compactification can be linked to Cartan holonomy reduction. This leads to a conceptual way to define other notions of geometric compactification. The idea will be taken up, in particular, for the case of compactifying pseudo‐Riemannian manifolds using projective geometry. A new characterisation of projectively compact metrics will be given, and some results on their asymptotics near the conformal infinity. This is joint work with Andreas Cap.