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?
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2$\begingroup$ 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. $\endgroup$– Greg FriedmanCommented Sep 4, 2016 at 5:41
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4$\begingroup$ 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. $\endgroup$– Greg FriedmanCommented Sep 4, 2016 at 5:44
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$\begingroup$ I wonder if this is written up anywhere. $\endgroup$– 54321userCommented Dec 10, 2016 at 23:36
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