The weight filtration for real algebraic varieties

Abstract

Using the work of Guillen and Navarro Aznar we associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on Borel-Moore homology with Z/2 coefficients an analog of the weight filtration for complex algebraic varieties.

29 pages. Improved discussions: weight spectral sequence (Proposition 1.8), Nash constructible functions (Theorem 3.4). New section on virtual Poincare polynomial (section 4.1)