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Apr 10, 2011 at 22:20 comment added John Klein @Neil: just a minor comment: both answers are really the same. If we put $-TM$ in dimension $-d$ then we get $H^*(M^{-TM})$ coincides with $H^{*+d}(M;\mathcal{L})$ where $\mathcal{L}$ is the orientation sheaf.
Apr 10, 2011 at 12:32 history answered Neil Strickland CC BY-SA 3.0