Constructing gravity amplitudes from real soft and collinear factorization

Soft and collinear factorizations can be used to construct expressions for amplitudes in theories of gravity. We generalise the ``half-soft'' functions used previously to ``soft-lifting'' functions and use these to generate tree and one-loop amplitudes. In particular we construct expressions for maximally helicity-violating tree amplitudes and the rational terms in one-loop amplitudes in the specific context of N=4 supergravity. To completely determine the rational terms collinear factorization must also be used. The rational terms for N=4 have a remarkable diagrammatic interpretation as arising from algebraic link diagrams.