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Apr 13, 2021 at 8:56 comment added Dan Petersen The result is true without assuming that the spaces are smooth. It follows from the Leray spectral sequence for compact support cohomology.
Apr 13, 2021 at 8:22 history edited Sean Lawton CC BY-SA 4.0
Added the statement of the theorem from the reference.
Apr 13, 2021 at 7:59 history answered Sean Lawton CC BY-SA 4.0