Virtual Betti numbers of real algebraic varieties

Mathematics – Algebraic Geometry

Scientific paper

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13 pages. Talk by first author, AMS meeting, Northeastern University, October 5-6, 2002

Scientific paper

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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