What I mean by QG (quantum geometry = quantum gravity) is an approach that provides some type of quantum universe model. So at a minimum there is a mathematical model of the continuum, with geometric measurements (such as area, volume, the dimensionality at a given location) represented by operators, as quantum observables. The quantum state of the universe's geometry appears in some form, in the theory. In a relativist context the geometry is the same thing as the gravitational field which is where the (QG = QG) equation comes from. Periodically we try to summarize and report what the current map of QG looks like and what the main directions are. There have been several past threads about this, but they are way out of date. The field has been moving along pretty fast and the job of scoping it out has been getting easier because there are signs of convergence. The main initiatives are Loops QG, Loll's Blocks QG, Reuter's Fixedpoint QG, and Connes' Noncommutative Geometry. The LOW BACKGROUND idea is, I think, well understood. To make a mathematical model of the continuum, or to represent dynamically changing geometry, you need some mathematical ground to build on. There is a choice of what and how much structure you invoke at the start, to launch the construction. For example you can start with a topological space like S3 that doesn't even come with coordinates: no differential structure, no implied smoothness! No geometry either. Geomety only comes if you further impose a metric, a distance function, or reasonable facsimile thereof. So maybe your theory doesn't get off the ground with a mere topological space, and you require more---eg some smooth differential structure, coordinates, calculus tools. Or you can assume even more---a fixed metric etc. (The approaches we're discussing here don't do that.) ========================= I believe General Relativity was the first physics theory to be low background in the sense that it does not require a fixed geometry to get started. It builds on a differential manifold---there are indeed coordinates with some smooth structure allowing calculus---but the manifold is limp and shapeless. It has no metric--no geometry. In GR the metric arises dynamically, as a solution to the main equation. So for the first time, a physical theory is constructed without predetermined geometry. The gravitational field is represented by the geometry itself. Since the only thing that matters then is the field, it is abstracted, freed of dependence on any particular manifold, and becomes the focus of attention. The manifold? a temporary convenience, downplayed and easily replaced. Low background QG approaches follow the lead of GR in that none of them declare a metric. In some respects they may be even leaner than their role-model GR. In any case there is no background spacetime, in the sense of a geometric setup. How could the initial background be made even leaner?--even more barren of structure. If you take a limp differential manifold (like what GR starts with) having, as we said, no metric geometry specified, and want to make it even more nondescript, you can strip off the coordinates and the differential calculus structure. Then all you have left is a topological space. That, for example, is what Loll's building block QG starts with. Typically spacetime is treated as S3 x R1, and a geometry is imposed on it by triangulating it with equal size blocks. A spacetime geometry is viewed as a path of evolution from some initial spatial configuration to a final one. Each path has an amplitude. The approach is closely analogous to a Feynman path integral.