# Is there a spectral sequence for borel-moore homology associated to a whitney filtration?

Consider a Whitney stratified space $$\varnothing = X_{-1} \subseteq X_0 \subseteq X_1 \subseteq \cdots \subseteq X_n$$ is there a spectral sequence for borel-moore homology which depends on the stratification on $X$? If so, where can I find more information about it?

• If each inclusion is a proper embedding (which I think it should be), I don't see why you wouldn't get the usual homology spectral sequence associated to a filtration. – Greg Friedman Sep 4 '16 at 5:41
• In particular, if the embedding is proper then you should have $C^{BM}_*(X_i)\subset C^{BM}_*(X_{i+1})$ for all $i$ and then the usual machinery applies to the filtered chain complex you get. – Greg Friedman Sep 4 '16 at 5:44
• I wonder if this is written up anywhere. – 54321user Dec 10 '16 at 23:36