Estimates of Characteristic numbers of real algebraic varieties
  We give some explicit bounds for the number of cobordism classes of real algebraic manifolds of real degree less than $d$, and for the size of the sum of $\mod 2$ Betti numbers for the real form of complex manifolds of complex degree less than $d$. 
Yves Laszlo (CMLS), Claude Viterbo (CMLS)