Andy Cap (Vienna): Asymptotic invariants of metrics

Motivated by the concept of mass for asymptotically hyperbolic metrics, we study invariants of pairs of metrics that are asymptotic to a certain order. We work in the setting of conformally compact metrics on arbitrary manifolds with boundary (at infinity). We need all metrics to be asymptotically hyperbolic in a very weak sense and then look at a class of metrics that are asymptotic to an appropriate higher order. This in particular ensures that all the metrics in the class induce the same conformal infinity on the boundary, and we construct local invariants as tractors for this conformal structure.
In the general setting (no restriction on the topology or further restrictions on the class) we obtain local invariants for pairs of metrics which satisfy a cocycle condition and remain unchanged if one of the factors is pulled back along a diffeomorphism that is asymptotic to the identity. In the special case that of the closed ball and a class of metrics containing a hyperbolic metric, we recover the classical mass of metrics in the class via an integral (in an appropriate sense) of our invariant.