Virtual Betti numbers of real algebraic varieties
Abstract
The weak factorization theorem for birational maps is used to prove that for all nonnegative i the ith mod 2 Betti number of compact nonsingular real algebraic varieties has a unique extension to a "virtual Betti number" betai defined for all real algebraic varieties, such that if Y is a closed subvariety of X, then betai(X) = betai(X) + betai(Y).
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