Let K be an arbitrary infinite field. The cohomology group \(H^{2}(SL(2,K);H_2 SL(2,K))\) contains the class of the universal central extension. When studying representations of fundamental groups of surfaces in SL(2, K) it is useful to have classes stable under deformations (Fenchel-Nielsen twists) of representations. We identify the maximal quotient of the universal class which is stable under twists as the Witt class of Nekovàř. The Milnor-Wood inequality asserts that an \(SL(2,\textbf{R})\) -bundle over a surface of genus g admits a flat structure if and only if its Euler number is \(\le (g - 1)\) . We establish an analog of this inequality, and a saturation result for the Witt class. The result is sharp for the field of rationals, but not sharp in general.
