  Quotients $Y=X/conj$ of complex surfaces by anti-holomorphic involutions
$conj\: X\to X$ tend to be completely decomposable when they are simply
connected, i.e., split into connected sums, $n CP^2\#m\barCP2$, if
$w_2(Y)\ne0$, or into $n(S^2\times S^2)$ if $w_2(Y)=0$. If $X$ is a double
branched covering over $CP^2$, this phenomenon is related to unknottedness of
Arnold surfaces in $S^4=CP^2/conj$, which was conjectured by V.Rokhlin. The
paper contains proof of Rokhlin Conjecture and of decomposability of quotients
for plenty of double planes and in certain other cases. This results give, in
particular, an elementary proof of Donaldson's result on decomposability of $Y$
for K3 surfaces.
