# Weight Filtrations for Real Algebraic Varieties

## Seminar/Forum

213
Peter Hall

For real algebraic varieties, we define a functorial weight filtration on homologies with Z/2 coefficients. This filtration is an analog of Deligne's weight filtration for complex algebraic varieties and can be defined on classical homologies and on Borel-Moore homologies. We show that the weight filtration on Borel-Moore homologies is induced by a geometric functorial filtration on the complex of semialgebraic chains with closed support. The associated spectral sequence gives non-trivial additive invariants of real algebraic varieties, the virtual Betti numbers. These additive invariants are used to classify the singularities of real analytic function germs by the method of motivic integration. (This is a joint work with Clint McCrory)

## Presenter

• Professor Adam Parusinski, Université Nice