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My book is Differential Forms in Algebraic Topology by Loring W. Tu and Raoul Bott of which An Introduction to Manifolds by Tu is a prequel.

Is there a good list of errata for Bott and Tu available? A cursory Google search reveals not much except this: Some possible mistakes in Bott and Tu, and possibly more here though uncompiled. Is there any source available online which lists inaccuracies and gaps?

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    $\begingroup$ The question might be reasonable, but regarding "I'm hoping something off topic on stackexchange would be on topic on overflow." <-- anything on-topic at MathOverflow is on-topic at math.SE, though the attention it might receive is different. If it's legitimately off-topic there, then it's off-topic here. And note that old questions from almost 9 years ago are not necessarily a good guide to what is now accepted. $\endgroup$ – David Roberts Jun 3 at 5:45
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    $\begingroup$ I will just mention that this book has an entry in Math Book Notes Wiki: Bott and Tu - Differential Forms in Algebraic Topology. $\endgroup$ – Martin Sleziak Jun 3 at 5:50
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    $\begingroup$ @DavidRoberts "anything on-topic at MathOverflow is on-topic at math.SE": well, almost. For instance math.stackexchange.com/questions/3135015 (now open) has been closed 3 times in MathSE (by 15 users) while probably nobody here would have the idea of closing it. $\endgroup$ – YCor Jun 3 at 7:17
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    $\begingroup$ I thought M.SE was for mathematics questions at all levels? Or is that a euphemism? $\endgroup$ – David Roberts Jun 3 at 8:02
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    $\begingroup$ As differences between (closures of posts on) MO and MSE seem to be a tangential topic to the question at hand, I have posted some comments on this in chat rather than continuing the discussion here. $\endgroup$ – Martin Sleziak Jun 3 at 8:29
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In page 18 (proof of Example 1.6), they claim "there are no constant functions on R1 with compact support" when they should have said "there are no nonzero constant..." This is confirmed in this question.

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In section 5, the closed Poincaré dual should be characterized with $\int_M \eta_S \wedge \omega $ and not $\int_M \omega \wedge \eta_S$.

As for the implications on the compact Poincaré dual, I'm waiting for answers or comments here: Closed Poincaré dual is $\int_M \eta_S \wedge \omega $ and not $\int_M \omega \wedge \eta_S$. What about the compact Poincaré dual?

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Here is the comment to this book in author's web page:

Differential Forms in Algebraic Topology (with Raoul Bott), third corrected printing, Graduate Text in Mathematics, Springer, New York, 1995.

The third printing published in 1995 corrects misprints in earlier printings; after that, the book has remained stable. Any printing dated 1995 or later should be fine. Earlier printings should be discarded.

Also you can check my web page for all possible math books errata (not completed yet).

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