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" 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).

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

References in corpus (3)

• An introduction to motivic integration
• Topology of singular algebraic varieties
• The universal Euler characteristic for varieties of characteristic zero

Cited by in corpus (2)

• A motivic approach to phase transitions in Potts models
• Motivic integration and Milnor fiber