Apparently I cannot get the right sign in deriving classical Gauss-Bonnet from generalised one!

According to many references (e.g. Madsen and Tornehave, Nakahara, Milnor and Stasheff if you don't use their particular convention about orientation) generalised Gauss-Bonnet is

$\int_M Pf(-R/2\pi)=\chi(M)$

where $R$ is the curvature 2-form and the Pfaffian of a 2lx2l antisymmetric matrix is $Pf(A)=\frac{1}{2^ll!}\epsilon ^{i_1 \ldots i_{2l}}A_{i_1 i_2} \ldots A_{i_{2l-1}i_{2l}} \ $ i.e. the sign convention is such that for the matrix A={{0,a},{-a,0}} Pf(A)=a.

For l=1, M is a surface and $R^a_{\phantom{a}b}=\frac{1}{2}R^a_{\phantom{a}bcd}e^c\wedge e^d =K (g_{ac}g_{bd}-g_{ad}g_{bc})$ where $K$ is the Gaussian curvature, $g_{ab}$ the metric tensor and $\{e^a\}$ an orthonormal basis. For the Pfaffian I get $Pf(-R/2 \pi)= -\frac{1}{4\pi} 2 \epsilon_{12} R^1_2= -\frac{1}{2\pi} R^1_{\phantom{1}2}=-\frac{1}{2\pi}R^1_{\phantom{1}212}e^1\wedge e^2$

$e^1\wedge e^2 $ is the volume form and $R^1_{\phantom{1}212}=K$ therefore

$\int_M Pf(-R/2\pi)=\int_M-K/2\pi=\chi$

which obviously has the wrong sign! I have carefully checked the definitions in the books and I think I am using the same as they use - so please be very explicit in pointing aout where the mistake is! Thanks