For algebraic invariants see algebraic topology. Donaldson also derived polynomial invariants from gauge theory. Differential topology is the study of global geometric invariants without a metric or symplectic form. There, groups are used to describe certain invariants of topological spaces. Curvature and torsion are the main invariants of an affine connection. Important invariants include knot polynomials, knot groups, and hyperbolic invariants. These can therefore serve as isomorphism invariants of graphs. Noether used these sorts of symmetries in her work on invariants in physics. It can be seen as the study of certain kinds of invariants of large matrices. However, discrete complete invariants of multidimensional persistence modules do not exist. Some object oriented programming languages have a special syntax for specifying class invariants. One is that color information is faster to compute compared to other invariants. All invariants of a smooth closed manifold are thus global. Combined they make the invariants of U("n") which is a subgroup of both these groups. This has important applications to the study of invariants in many fields of mathematics.