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. Neither of which appears to have an official errata list. However, the prequel has an unofficial errata list, and the few errors I've found in the prequel (like this) don't appear to have been asked about before.
Now the book appears to have some errors that are asked about on stackexchange already. Twice now I've typed up questions that turn out to have been asked about already. One of which is a confirmed error. There could be a lot more here https://math.stackexchange.com/search?q=bott+tu (like this), but there's no specific order, and I don't imagine I can search only for the ones in a particular Chapter or Section.
Recently, I tried to come up with an errata on stackexchange, but my question Errata for Bott Tu Differential Forms was put on hold even though Errata for Atiyah-Macdonald on overflow is just fine. I'm assuming there isn't a difference between stackexchange and overflow for this case because so far no one suggested for me to ask on overflow instead.
It seems like wasting a lot of thousands of readers' time that to try to understand something in a textbook that
turns out to be an error
is apparently asked about somewhere on stackexchange or physicsforums.
There's nothing really one can do about
errors one realizes but no one has asked so far (like this)
errors that one doesn't even realize until 17 sections later (like this)
possible errors one suspects but which one thinks is kind of obvious, in which case I think we can kind of apply this Why do so many textbooks have so much technical detail and so little enlightenment? to think "It's not really worth typing it up on stackexchange, so I'll assume it's an error until there's evidence otherwise"
But for errors that people have already spent so much time inventing a wheel for, how does one avoid reinventing the wheel i.e. avoid spending time asking questions about something that turns out to be an error already asked about on stackexchange?
Some notes and guide questions to address the main question in the preceding paragraph.
Does one really look up every single question on that mentions the book like this https://math.stackexchange.com/search?q=bott+tu? So far we don't have an "error" tag for questions where it turns out that the book has made an error.
Should we study only books that have either official errata and an errata on stackexchange or overflow?
Could be relevant: (I didn't have much of a problem with An Introduction to Manifolds by Loring W. Tu, but I did with From Calculus to Cohomology by Ib Madsen and Jørgen Tornehave such as with the term "positively oriented".
If you are having so many issues with the definitions in a given textbook, it might be a good time to pick up another book. There are so many introductory smooth manifold texts to choose from. The world is your oyster. – AnonymousCoward May 10 at 13:35
I guess we apply the concept from "definitions" to "errors".
My recent question: Errata for Bott Tu Differential Forms in Algebraic Topology
Note: I'm not asking "Why don't authors have an official errata?" or "Why doesn't stackexchange/overflow allow this?" I'm asking what one should do given that compiling isn't allowed and there is no official errata in the situations where there will definitely be an error that is already asked about but is not readily accessible in some arranged or at least compiled format.
Imagine thousands of readers all having the same question as I did here, where I spent 2.5 hours trying to understand it and 1 hour typing it up. This would be 3,500 hours of time wasted.