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Virtual Betti numbers of real algebraic varieties

Clint McCrory·Adam Parusinski
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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" beta_i defined for all real algebraic varieties, such that if Y is a closed subvariety of X, then beta_i(X) = beta_i(X\Y) + beta_i(Y).

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Clint McCrory, Adam Parusinski. 2002-10-23. Virtual Betti numbers of real algebraic varieties. https://arxiv.org/abs/math/0210374

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