This question might be the same as this: Definition of closed Poincaré dual (I didn't read too carefully) but there is no answer.
My book is Differential Forms in Algebraic Topology by Loring W. Tu and Raoul Bott of which An Introduction to Manifolds by Loring W. Tu is a prequel.
The characterization of the closed Poincaré dual is given here (the "(5.13)") in Section 5.5. This has $\int_M \omega \wedge \eta_S$, where $\eta_S$ is on the right rather than left.
Question: Why is it $\int_M \omega \wedge \eta_S$, where $\eta_S$ is on the right rather than left?
- Update: The book made a mistake. See my question on overflow.