A brief note on how Einstein's general relativity has influenced the development of modern differential geometry

Holographic Special Relativity

We reinterpret special relativity, or more precisely its de Sitter deformation, in terms of 3d conformal geometry, as opposed to (3+1)d spacetime geometry. An inertial observer, usually described by a geodesic in spacetime, becomes instead a choice of ways to reverse the conformal compactification of a Euclidean vector space up to scale. The observer's "current time," usually given by a point along the geodesic, corresponds to the choice of scale in the decompactification. We also show how arbitrary conformal 3-geometries give rise to "observer space geometries," as defined in recent work, fro…